LMFDB - Embedded newform 875.2.bb.c.493.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [875,2,Mod(82,875)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("875.82"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(875, base_ring=CyclotomicField(60)) chi = DirichletCharacter(H, H._module([27, 50])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 875 = 5^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	875.bb (of order $60$, degree $16$, not minimal)

Newform invariants

comment:select newform

sage:traces = [288,8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.98691017686$
Analytic rank:	$0$
Dimension:	$288$
Relative dimension:	$18$ over $\Q(\zeta_{60})$
Twist minimal:	no (minimal twist has level 175)
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			493.5
Character	$\chi$	$=$	875.493
Dual form			875.2.bb.c.607.5

$q$-expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.882496 + 1.35892i) q^{2} +(0.978941 - 2.55023i) q^{3} +(-0.254403 - 0.571398i) q^{4} +(2.60166 + 3.58087i) q^{6} +(2.64114 - 0.156130i) q^{7} +(-2.19977 - 0.348409i) q^{8} +(-3.31591 - 2.98566i) q^{9} +(2.62811 + 2.91881i) q^{11} +(-1.70624 + 0.0894203i) q^{12} +(-0.0865535 - 0.0441012i) q^{13} +(-2.11863 + 3.72689i) q^{14} +(3.25179 - 3.61148i) q^{16} +(-2.10918 + 2.60462i) q^{17} +(6.98356 - 1.87124i) q^{18} +(5.56832 + 2.47917i) q^{19} +(2.18736 - 6.88836i) q^{21} +(-6.28573 + 0.995562i) q^{22} +(4.39848 + 2.85640i) q^{23} +(-3.04197 + 5.26884i) q^{24} +(0.136313 - 0.0787005i) q^{26} +(-3.55840 + 1.81310i) q^{27} +(-0.761125 - 1.46942i) q^{28} +(2.51245 - 3.45809i) q^{29} +(-0.701840 + 0.0737664i) q^{31} +(0.885159 + 3.30346i) q^{32} +(10.0164 - 3.84493i) q^{33} +(-1.67814 - 5.16477i) q^{34} +(-0.862422 + 2.65426i) q^{36} +(-0.403914 - 7.70713i) q^{37} +(-8.28302 + 5.37906i) q^{38} +(-0.197199 + 0.177559i) q^{39} +(-0.124652 + 0.0405019i) q^{41} +(7.43042 + 9.05139i) q^{42} +(-8.25770 - 8.25770i) q^{43} +(0.999203 - 2.24425i) q^{44} +(-7.76327 + 3.45643i) q^{46} +(-2.10528 + 1.70482i) q^{47} +(-6.02679 - 11.8282i) q^{48} +(6.95125 - 0.824720i) q^{49} +(4.57761 + 7.92865i) q^{51} +(-0.00317989 + 0.0606759i) q^{52} +(10.9795 + 4.21462i) q^{53} +(0.676413 - 6.43564i) q^{54} +(-5.86430 - 0.576749i) q^{56} +(11.7735 - 11.7735i) q^{57} +(2.48206 + 6.46598i) q^{58} +(-5.04772 - 1.07293i) q^{59} +(-1.48307 - 6.97731i) q^{61} +(0.519128 - 1.01885i) q^{62} +(-9.22393 - 7.36783i) q^{63} +(3.97346 + 1.29105i) q^{64} +(-3.61445 + 17.0046i) q^{66} +(-0.433773 - 0.351262i) q^{67} +(2.02485 + 0.542557i) q^{68} +(11.5903 - 8.42087i) q^{69} +(0.818370 + 0.594581i) q^{71} +(6.25400 + 7.72305i) q^{72} +(2.13084 + 0.111673i) q^{73} +(10.8299 + 6.25262i) q^{74} -3.81243i q^{76} +(7.39691 + 7.29866i) q^{77} +(-0.0672616 - 0.424673i) q^{78} +(15.3675 + 1.61519i) q^{79} +(-0.258873 - 2.46301i) q^{81} +(0.0549659 - 0.205136i) q^{82} +(-1.69214 + 10.6837i) q^{83} +(-4.49246 + 0.502566i) q^{84} +(18.5090 - 3.93420i) q^{86} +(-6.35939 - 9.79260i) q^{87} +(-4.76429 - 7.33636i) q^{88} +(-0.981714 + 0.208670i) q^{89} +(-0.235485 - 0.102964i) q^{91} +(0.513159 - 3.23996i) q^{92} +(-0.498939 + 1.86207i) q^{93} +(-0.458824 - 4.36542i) q^{94} +(9.29110 + 0.976534i) q^{96} +(1.77133 + 11.1837i) q^{97} +(-5.01371 + 10.1740i) q^{98} -17.5251i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q + 8 q^{2} + 24 q^{3} - 10 q^{4} + 10 q^{7} + 36 q^{8} - 10 q^{9} - 6 q^{11} + 36 q^{12} - 20 q^{14} - 30 q^{16} + 42 q^{17} + 14 q^{18} - 30 q^{19} - 12 q^{21} - 32 q^{22} + 40 q^{23} - 48 q^{26}+ \cdots - 222 q^{98}+O(q^{100}) $ 288 * q + 8 * q^2 + 24 * q^3 - 10 * q^4 + 10 * q^7 + 36 * q^8 - 10 * q^9 - 6 * q^11 + 36 * q^12 - 20 * q^14 - 30 * q^16 + 42 * q^17 + 14 * q^18 - 30 * q^19 - 12 * q^21 - 32 * q^22 + 40 * q^23 - 48 * q^26 - 22 * q^28 - 18 * q^31 - 8 * q^32 + 30 * q^33 + 40 * q^36 + 10 * q^37 - 72 * q^38 + 30 * q^39 - 6 * q^42 + 108 * q^43 - 10 * q^44 - 6 * q^46 + 54 * q^47 - 16 * q^51 - 216 * q^52 - 50 * q^53 - 30 * q^54 + 4 * q^56 + 216 * q^57 + 4 * q^58 + 90 * q^59 - 18 * q^61 + 66 * q^63 - 100 * q^64 - 90 * q^66 - 4 * q^67 - 342 * q^68 - 24 * q^71 - 58 * q^72 + 6 * q^73 + 80 * q^77 + 132 * q^78 - 10 * q^79 - 10 * q^81 - 216 * q^82 + 20 * q^84 - 6 * q^86 + 48 * q^87 + 122 * q^88 + 120 * q^89 - 12 * q^91 + 4 * q^92 - 106 * q^93 - 30 * q^94 - 90 * q^96 - 222 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/875\mathbb{Z}\right)^\times$.

$n$	$127$	$626$
$\chi(n)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.882496	+	1.35892i	−0.624019	+	0.960904i	0.375402	+	0.926862i	$0.377505\pi$
$2$	−0.882496	+	1.35892i	−0.624019	+	0.960904i	−0.999420	+	0.0340422i	$0.989162\pi$
$3$	0.978941	−	2.55023i	0.565192	−	1.47238i	−0.291512	−	0.956567i	$-0.594158\pi$
$3$	0.978941	−	2.55023i	0.565192	−	1.47238i	0.856704	−	0.515808i	$-0.172508\pi$
$4$	−0.254403	−	0.571398i	−0.127201	−	0.285699i
$5$		0			0
$5$		0			0
$6$	2.60166	+	3.58087i	1.06212	+	1.46189i
$7$	2.64114	−	0.156130i	0.998257	−	0.0590114i
$7$	2.64114	−	0.156130i	0.998257	−	0.0590114i
$8$	−2.19977	−	0.348409i	−0.777736	−	0.123181i
$9$	−3.31591	−	2.98566i	−1.10530	−	0.995219i
$10$		0			0
$11$	2.62811	+	2.91881i	0.792404	+	0.880054i	0.995068	−	0.0991947i	$-0.0316267\pi$
$11$	2.62811	+	2.91881i	0.792404	+	0.880054i	−0.202664	+	0.979248i	$0.564960\pi$
$12$	−1.70624	+	0.0894203i	−0.492549	+	0.0258134i
$13$	−0.0865535	−	0.0441012i	−0.0240056	−	0.0122315i	0.441946	−	0.897041i	$-0.354288\pi$
$13$	−0.0865535	−	0.0441012i	−0.0240056	−	0.0122315i	−0.465952	+	0.884810i	$0.654288\pi$
$14$	−2.11863	+	3.72689i	−0.566227	+	0.996054i
$15$		0			0
$16$	3.25179	−	3.61148i	0.812948	−	0.902871i
$17$	−2.10918	+	2.60462i	−0.511550	+	0.631712i	−0.965839	−	0.259142i	$-0.916560\pi$
$17$	−2.10918	+	2.60462i	−0.511550	+	0.631712i	0.454289	+	0.890854i	$0.349893\pi$
$18$	6.98356	−	1.87124i	1.64604	−	0.441055i
$19$	5.56832	+	2.47917i	1.27746	+	0.568762i	0.929526	−	0.368757i	$-0.120217\pi$
$19$	5.56832	+	2.47917i	1.27746	+	0.568762i	0.347934	+	0.937519i	$0.386883\pi$
$20$		0			0
$21$	2.18736	−	6.88836i	0.477320	−	1.50316i
$22$	−6.28573	+	0.995562i	−1.34012	+	0.212254i
$23$	4.39848	+	2.85640i	0.917146	+	0.595601i	0.914584	−	0.404395i	$-0.132518\pi$
$23$	4.39848	+	2.85640i	0.917146	+	0.595601i	0.00256149	+	0.999997i	$0.499185\pi$
$24$	−3.04197	+	5.26884i	−0.620939	+	1.07550i
$25$		0			0
$26$	0.136313	−	0.0787005i	0.0267332	−	0.0154344i
$27$	−3.55840	+	1.81310i	−0.684814	+	0.348930i
$28$	−0.761125	−	1.46942i	−0.143839	−	0.277695i
$29$	2.51245	−	3.45809i	0.466550	−	0.642152i	−0.509301	−	0.860589i	$-0.670096\pi$
$29$	2.51245	−	3.45809i	0.466550	−	0.642152i	0.975851	+	0.218437i	$0.0700959\pi$
$30$		0			0
$31$	−0.701840	+	0.0737664i	−0.126054	+	0.0132488i	−0.167345	−	0.985898i	$-0.553520\pi$
$31$	−0.701840	+	0.0737664i	−0.126054	+	0.0132488i	0.0412913	+	0.999147i	$0.486853\pi$
$32$	0.885159	+	3.30346i	0.156475	+	0.583975i
$33$	10.0164	−	3.84493i	1.74363	−	0.669317i
$34$	−1.67814	−	5.16477i	−0.287798	−	0.885751i
$35$		0			0
$36$	−0.862422	+	2.65426i	−0.143737	+	0.442377i
$37$	−0.403914	−	7.70713i	−0.0664030	−	1.26704i	−0.805154	−	0.593066i	$-0.797917\pi$
$37$	−0.403914	−	7.70713i	−0.0664030	−	1.26704i	0.738751	−	0.673978i	$-0.235416\pi$
$38$	−8.28302	+	5.37906i	−1.34368	+	0.872599i
$39$	−0.197199	+	0.177559i	−0.0315771	+	0.0284322i
$40$		0			0
$41$	−0.124652	+	0.0405019i	−0.0194674	+	0.00632534i	−0.318735	−	0.947844i	$-0.603258\pi$
$41$	−0.124652	+	0.0405019i	−0.0194674	+	0.00632534i	0.299267	+	0.954169i	$0.403258\pi$
$42$	7.43042	+	9.05139i	1.14654	+	1.39666i
$43$	−8.25770	−	8.25770i	−1.25929	−	1.25929i	−0.951434	−	0.307854i	$-0.900389\pi$
$43$	−8.25770	−	8.25770i	−1.25929	−	1.25929i	−0.307854	−	0.951434i	$-0.599611\pi$
$44$	0.999203	−	2.24425i	0.150636	−	0.338333i
$45$		0			0
$46$	−7.76327	+	3.45643i	−1.14463	+	0.509623i
$47$	−2.10528	+	1.70482i	−0.307087	+	0.248674i	−0.770459	−	0.637490i	$-0.779973\pi$
$47$	−2.10528	+	1.70482i	−0.307087	+	0.248674i	0.463372	+	0.886164i	$0.346639\pi$
$48$	−6.02679	−	11.8282i	−0.869893	−	1.70726i
$49$	6.95125	−	0.824720i	0.993035	−	0.117817i
$50$		0			0
$51$	4.57761	+	7.92865i	0.640993	+	1.11023i
$52$	−0.00317989	+	0.0606759i	−0.000440972	+	0.00841424i
$53$	10.9795	+	4.21462i	1.50814	+	0.578922i	0.965354	−	0.260945i	$-0.0840342\pi$
$53$	10.9795	+	4.21462i	1.50814	+	0.578922i	0.542791	+	0.839868i	$0.317368\pi$
$54$	0.676413	−	6.43564i	0.0920482	−	0.875780i
$55$		0			0
$56$	−5.86430	−	0.576749i	−0.783649	−	0.0770713i
$57$	11.7735	−	11.7735i	1.55944	−	1.55944i
$58$	2.48206	+	6.46598i	0.325910	+	0.849025i
$59$	−5.04772	−	1.07293i	−0.657157	−	0.139683i	−0.132748	−	0.991150i	$-0.542380\pi$
$59$	−5.04772	−	1.07293i	−0.657157	−	0.139683i	−0.524409	+	0.851467i	$0.675714\pi$
$60$		0			0
$61$	−1.48307	−	6.97731i	−0.189888	−	0.893354i	−0.965147	−	0.261709i	$-0.915714\pi$
$61$	−1.48307	−	6.97731i	−0.189888	−	0.893354i	0.775259	−	0.631644i	$-0.217620\pi$
$62$	0.519128	−	1.01885i	0.0659293	−	0.129394i
$63$	−9.22393	−	7.36783i	−1.16211	−	0.928260i
$64$	3.97346	+	1.29105i	0.496682	+	0.161382i
$65$		0			0
$66$	−3.61445	+	17.0046i	−0.444908	+	2.09313i
$67$	−0.433773	−	0.351262i	−0.0529938	−	0.0429135i	0.602458	−	0.798151i	$-0.294188\pi$
$67$	−0.433773	−	0.351262i	−0.0529938	−	0.0429135i	−0.655451	+	0.755237i	$0.727522\pi$
$68$	2.02485	+	0.542557i	0.245549	+	0.0657947i
$69$	11.5903	−	8.42087i	1.39531	−	1.01375i
$70$		0			0
$71$	0.818370	+	0.594581i	0.0971227	+	0.0705637i	0.635287	−	0.772276i	$-0.280882\pi$
$71$	0.818370	+	0.594581i	0.0971227	+	0.0705637i	−0.538164	+	0.842840i	$0.680882\pi$
$72$	6.25400	+	7.72305i	0.737041	+	0.910170i
$73$	2.13084	+	0.111673i	0.249396	+	0.0130703i	0.176624	−	0.984278i	$-0.443482\pi$
$73$	2.13084	+	0.111673i	0.249396	+	0.0130703i	0.0727716	+	0.997349i	$0.476816\pi$
$74$	10.8299	+	6.25262i	1.25894	+	0.726852i
$75$		0			0
$76$		−	3.81243i		−	0.437316i
$77$	7.39691	+	7.29866i	0.842956	+	0.831759i
$78$	−0.0672616	−	0.424673i	−0.00761588	−	0.0480848i
$79$	15.3675	+	1.61519i	1.72898	+	0.181723i	0.916167	−	0.400797i	$-0.131267\pi$
$79$	15.3675	+	1.61519i	1.72898	+	0.181723i	0.812816	+	0.582521i	$0.197933\pi$
$80$		0			0
$81$	−0.258873	−	2.46301i	−0.0287636	−	0.273668i
$82$	0.0549659	−	0.205136i	0.00606997	−	0.0226534i
$83$	−1.69214	+	10.6837i	−0.185736	+	1.17269i	0.701944	+	0.712232i	$0.252316\pi$
$83$	−1.69214	+	10.6837i	−0.185736	+	1.17269i	−0.887680	+	0.460461i	$0.847684\pi$
$84$	−4.49246	+	0.502566i	−0.490168	+	0.0548345i
$85$		0			0
$86$	18.5090	−	3.93420i	1.99587	−	0.424236i
$87$	−6.35939	−	9.79260i	−0.681798	−	1.04988i
$88$	−4.76429	−	7.33636i	−0.507875	−	0.782058i
$89$	−0.981714	+	0.208670i	−0.104061	+	0.0221190i	−0.259648	−	0.965703i	$-0.583607\pi$
$89$	−0.981714	+	0.208670i	−0.104061	+	0.0221190i	0.155587	+	0.987822i	$0.450273\pi$
$90$		0			0
$91$	−0.235485	−	0.102964i	−0.0246856	−	0.0107936i
$92$	0.513159	−	3.23996i	0.0535005	−	0.337789i
$93$	−0.498939	+	1.86207i	−0.0517376	+	0.193087i
$94$	−0.458824	−	4.36542i	−0.0473241	−	0.450259i
$95$		0			0
$96$	9.29110	+	0.976534i	0.948269	+	0.0996670i
$97$	1.77133	+	11.1837i	0.179851	+	1.13554i	0.898113	+	0.439764i	$0.144938\pi$
$97$	1.77133	+	11.1837i	0.179851	+	1.13554i	−0.718262	+	0.695773i	$0.755062\pi$
$98$	−5.01371	+	10.1740i	−0.506461	+	1.02773i
$99$		−	17.5251i		−	1.76134i
$100$		0			0
$101$	−10.1623	−	5.86718i	−1.01118	−	0.583807i	−0.0996449	−	0.995023i	$-0.531771\pi$
$101$	−10.1623	−	5.86718i	−1.01118	−	0.583807i	−0.911538	+	0.411216i	$0.865104\pi$
$102$	−14.8141	−	0.776377i	−1.46682	−	0.0768727i
$103$	−6.33822	−	7.82705i	−0.624523	−	0.771222i	0.362468	−	0.931996i	$-0.381934\pi$
$103$	−6.33822	−	7.82705i	−0.624523	−	0.771222i	−0.986991	+	0.160774i	$0.948601\pi$
$104$	0.175032	+	0.127168i	0.0171633	+	0.0124699i
$105$		0			0
$106$	−15.4167	+	11.2009i	−1.49740	+	1.08792i
$107$	−1.09349	−	0.292999i	−0.105711	−	0.0283253i	0.205576	−	0.978641i	$-0.434093\pi$
$107$	−1.09349	−	0.292999i	−0.105711	−	0.0283253i	−0.311287	+	0.950316i	$0.600760\pi$
$108$	1.94126	+	1.57201i	0.186798	+	0.151266i
$109$	−0.608654	+	2.86349i	−0.0582985	+	0.274273i	−0.997636	−	0.0687217i	$-0.978108\pi$
$109$	−0.608654	+	2.86349i	−0.0582985	+	0.274273i	0.939337	+	0.342995i	$0.111441\pi$
$110$		0			0
$111$	−20.0504	−	6.51476i	−1.90310	−	0.618353i
$112$	8.02458	−	10.0461i	0.758252	−	0.949271i
$113$	2.12100	−	4.16270i	0.199527	−	0.391594i	−0.769464	−	0.638690i	$-0.779477\pi$
$113$	2.12100	−	4.16270i	0.199527	−	0.391594i	0.968991	+	0.247097i	$0.0794765\pi$
$114$	5.60924	+	26.3894i	0.525353	+	2.47159i
$115$		0			0
$116$	−2.61512	−	0.555861i	−0.242808	−	0.0516104i
$117$	0.155332	+	0.404655i	0.0143605	+	0.0374103i
$118$	5.91261	−	5.91261i	0.544300	−	0.544300i
$119$	−5.16397	+	7.20846i	−0.473381	+	0.660798i
$120$		0			0
$121$	−0.462683	+	4.40213i	−0.0420621	+	0.400194i
$122$	10.7904	+	4.14206i	0.976921	+	0.375005i
$123$	−0.0187379	+	0.357541i	−0.00168954	+	0.0322383i
$124$	0.220700	+	0.382263i	0.0198194	+	0.0343283i
$125$		0			0
$126$	18.1524	−	6.03254i	1.61714	−	0.537422i
$127$	7.51832	+	14.7555i	0.667143	+	1.30934i	0.937971	+	0.346713i	$0.112702\pi$
$127$	7.51832	+	14.7555i	0.667143	+	1.30934i	−0.270829	+	0.962628i	$0.587298\pi$
$128$	−10.5767	+	8.56482i	−0.934854	+	0.757030i
$129$	−29.1428	+	12.9752i	−2.56588	+	1.14240i
$130$		0			0
$131$	−0.163724	+	0.367729i	−0.0143046	+	0.0321287i	−0.920557	−	0.390609i	$-0.872264\pi$
$131$	−0.163724	+	0.367729i	−0.0143046	+	0.0321287i	0.906252	+	0.422738i	$0.138931\pi$
$132$	−4.74518	−	4.74518i	−0.413015	−	0.413015i
$133$	15.0938	+	5.67847i	1.30880	+	0.492386i
$134$	0.860142	−	0.279477i	0.0743049	−	0.0241431i
$135$		0			0
$136$	5.54717	−	4.99470i	0.475666	−	0.428292i
$137$	−10.6234	+	6.89895i	−0.907623	+	0.589417i	−0.911827	−	0.410574i	$-0.865328\pi$
$137$	−10.6234	+	6.89895i	−0.907623	+	0.589417i	0.00420463	+	0.999991i	$0.498662\pi$
$138$	1.21491	+	23.1818i	0.103420	+	1.97336i
$139$	−4.44619	+	13.6840i	−0.377121	+	1.16066i	0.564915	+	0.825149i	$0.308909\pi$
$139$	−4.44619	+	13.6840i	−0.377121	+	1.16066i	−0.942036	+	0.335511i	$0.891091\pi$
$140$		0			0
$141$	2.28674	+	7.03788i	0.192579	+	0.592696i
$142$	−1.53020	+	0.587388i	−0.128411	+	0.0492925i
$143$	−0.0987488	−	0.368536i	−0.00825779	−	0.0308185i
$144$	−21.5653	+	2.26661i	−1.79711	+	0.188884i
$145$		0			0
$146$	−2.03221	+	2.79710i	−0.168187	+	0.231489i
$147$	4.70164	−	18.5346i	0.387785	−	1.52871i
$148$	−4.30108	+	2.19151i	−0.353547	+	0.180141i
$149$	−9.24670	+	5.33859i	−0.757519	+	0.437354i	−0.828404	−	0.560131i	$-0.810751\pi$
$149$	−9.24670	+	5.33859i	−0.757519	+	0.437354i	0.0708851	+	0.997484i	$0.477418\pi$
$150$		0			0
$151$	−10.4396	+	18.0820i	−0.849565	+	1.47149i	0.0320315	+	0.999487i	$0.489802\pi$
$151$	−10.4396	+	18.0820i	−0.849565	+	1.47149i	−0.881597	+	0.472003i	$0.843531\pi$
$152$	−11.3852	−	7.39366i	−0.923465	−	0.599705i
$153$	14.7703	−	2.33939i	1.19411	−	0.189128i
$154$	−16.4461	+	3.61081i	−1.32526	+	0.290967i
$155$		0			0
$156$	0.151625	+	0.0675076i	0.0121397	+	0.00540494i
$157$	−11.5468	+	3.09395i	−0.921533	+	0.246924i	−0.688241	−	0.725483i	$-0.741617\pi$
$157$	−11.5468	+	3.09395i	−0.921533	+	0.246924i	−0.233293	+	0.972407i	$0.574950\pi$
$158$	−15.7567	+	19.4579i	−1.25354	+	1.54799i
$159$	21.4965	−	23.8743i	1.70478	−	1.89335i
$160$		0			0
$161$	12.0630	+	6.85743i	0.950695	+	0.540441i
$162$	3.57550	+	1.82181i	0.280918	+	0.143135i
$163$	14.4820	−	0.758967i	1.13431	−	0.0594469i	0.524081	−	0.851668i	$-0.324409\pi$
$163$	14.4820	−	0.758967i	1.13431	−	0.0594469i	0.610234	+	0.792222i	$0.291076\pi$
$164$	0.0548546	+	0.0609222i	0.00428342	+	0.00475722i
$165$		0			0
$166$	−13.0251	−	11.7278i	−1.01094	−	0.910257i
$167$	1.65219	+	0.261681i	0.127850	+	0.0202495i	0.220032	−	0.975493i	$-0.429384\pi$
$167$	1.65219	+	0.261681i	0.127850	+	0.0202495i	−0.0921813	+	0.995742i	$0.529384\pi$
$168$	−7.21164	+	14.3907i	−0.556390	+	1.11027i
$169$	−7.63566	−	10.5096i	−0.587359	−	0.808430i
$170$		0			0
$171$	−11.0621	−	24.8458i	−0.845937	−	1.90001i
$172$	−2.61765	+	6.81921i	−0.199594	+	0.519960i
$173$	0.153180	−	0.235876i	0.0116460	−	0.0179333i	−0.832800	−	0.553575i	$-0.813263\pi$
$173$	0.153180	−	0.235876i	0.0116460	−	0.0179333i	0.844446	+	0.535641i	$0.179930\pi$
$174$	18.9195			1.43429
$175$		0			0
$176$	19.0873			1.43876
$177$	−7.67763	+	11.8225i	−0.577086	+	0.888634i
$178$	0.582792	−	1.51822i	0.0436821	−	0.113796i
$179$	−5.33375	−	11.9798i	−0.398663	−	0.895412i	−0.995651	−	0.0931620i	$-0.970303\pi$
$179$	−5.33375	−	11.9798i	−0.398663	−	0.895412i	0.596988	−	0.802250i	$-0.296364\pi$
$180$		0			0
$181$	−13.5383	−	18.6338i	−1.00629	−	1.38504i	−0.921384	−	0.388653i	$-0.872940\pi$
$181$	−13.5383	−	18.6338i	−1.00629	−	1.38504i	−0.0849076	−	0.996389i	$-0.527060\pi$
$182$	0.347735	−	0.229142i	0.0257758	−	0.0169851i
$183$	−19.2456	−	3.04820i	−1.42268	−	0.225330i
$184$	−8.68043	−	7.81590i	−0.639930	−	0.576196i
$185$		0			0
$186$	−2.09009	−	2.32129i	−0.153253	−	0.170205i
$187$	−13.1455	+	0.688927i	−0.961295	+	0.0503793i
$188$	1.50972	+	0.769242i	0.110108	+	0.0561027i
$189$	−9.11516	+	5.34421i	−0.663030	+	0.388734i
$190$		0			0
$191$	2.70749	−	3.00698i	0.195907	−	0.217577i	−0.637185	−	0.770711i	$-0.719901\pi$
$191$	2.70749	−	3.00698i	0.195907	−	0.217577i	0.833093	+	0.553133i	$0.186568\pi$
$192$	7.18227	−	8.86936i	0.518335	−	0.640091i
$193$	2.96976	−	0.795745i	0.213768	−	0.0572790i	−0.150346	−	0.988634i	$-0.548039\pi$
$193$	2.96976	−	0.795745i	0.213768	−	0.0572790i	0.364114	+	0.931355i	$0.381372\pi$
$194$	−16.7611	−	7.46250i	−1.20337	−	0.535776i
$195$		0			0
$196$	−2.23966	−	3.76212i	−0.159976	−	0.268723i
$197$	−12.4561	+	1.97286i	−0.887464	+	0.140560i	−0.583490	−	0.812120i	$-0.698313\pi$
$197$	−12.4561	+	1.97286i	−0.887464	+	0.140560i	−0.303973	+	0.952681i	$0.598313\pi$
$198$	23.8153	+	15.4658i	1.69248	+	1.09911i
$199$	2.17496	−	3.76715i	0.154179	−	0.267046i	−0.778581	−	0.627545i	$-0.784060\pi$
$199$	2.17496	−	3.76715i	0.154179	−	0.267046i	0.932760	+	0.360498i	$0.117393\pi$
$200$		0			0
$201$	−1.32044	+	0.762355i	−0.0931365	+	0.0537724i
$202$	16.9412	−	8.63198i	1.19198	−	0.607344i
$203$	6.09583	−	9.52558i	0.427843	−	0.668564i
$204$	3.36586	−	4.63270i	0.235657	−	0.324354i
$205$		0			0
$206$	16.2298	−	1.70582i	1.13078	−	0.118850i
$207$	−6.05670	−	22.6039i	−0.420970	−	1.57108i
$208$	−0.440725	+	0.169178i	−0.0305588	+	0.0117304i
$209$	7.39789	+	22.7684i	0.511723	+	1.57492i
$210$		0			0
$211$	2.05986	−	6.33961i	0.141807	−	0.436437i	−0.854780	−	0.518991i	$-0.826308\pi$
$211$	2.05986	−	6.33961i	0.141807	−	0.436437i	0.996587	+	0.0825543i	$0.0263078\pi$
$212$	−0.384980	−	7.34585i	−0.0264405	−	0.504515i
$213$	2.31745	−	1.50497i	0.158789	−	0.103119i
$214$	1.36316	−	1.22740i	0.0931838	−	0.0839031i
$215$		0			0
$216$	8.45936	−	2.74861i	0.575586	−	0.187019i
$217$	−1.84214	+	0.304405i	−0.125053	+	0.0206644i
$218$	−3.35413	−	3.35413i	−0.227171	−	0.227171i
$219$	2.37076	−	5.32481i	0.160201	−	0.359817i
$220$		0			0
$221$	0.297423	−	0.132421i	0.0200069	−	0.00890762i
$222$	26.5474	−	21.4977i	1.78175	−	1.44283i
$223$	−6.99626	−	13.7309i	−0.468504	−	0.919491i	−0.997486	−	0.0708583i	$-0.977426\pi$
$223$	−6.99626	−	13.7309i	−0.468504	−	0.919491i	0.528982	−	0.848633i	$-0.322574\pi$
$224$	2.85360	+	8.58670i	0.190664	+	0.573723i
$225$		0			0
$226$	3.78502	+	6.55584i	0.251776	+	0.436088i
$227$	−0.693452	+	13.2319i	−0.0460260	+	0.878229i	0.873892	+	0.486119i	$0.161588\pi$
$227$	−0.693452	+	13.2319i	−0.0460260	+	0.878229i	−0.919918	+	0.392110i	$0.871745\pi$
$228$	−9.72258	−	3.73215i	−0.643893	−	0.247168i
$229$	−0.433550	+	4.12495i	−0.0286498	+	0.272584i	0.970814	+	0.239834i	$0.0770932\pi$
$229$	−0.433550	+	4.12495i	−0.0286498	+	0.272584i	−0.999464	+	0.0327499i	$0.989574\pi$
$230$		0			0
$231$	25.8544	−	11.7189i	1.70109	−	0.771044i
$232$	−6.73164	+	6.73164i	−0.441954	+	0.441954i
$233$	−9.23458	−	24.0569i	−0.604977	−	1.57602i	−0.803101	−	0.595843i	$-0.796818\pi$
$233$	−9.23458	−	24.0569i	−0.604977	−	1.57602i	0.198124	−	0.980177i	$-0.436515\pi$
$234$	−0.686975	−	0.146021i	−0.0449090	−	0.00954570i
$235$		0			0
$236$	0.671086	+	3.15721i	0.0436840	+	0.205517i
$237$	19.1630	−	37.6096i	1.24477	−	2.44300i
$238$	−5.23857	−	13.3789i	−0.339566	−	0.867224i
$239$	−0.618920	−	0.201099i	−0.0400346	−	0.0130080i	0.288931	−	0.957350i	$-0.406700\pi$
$239$	−0.618920	−	0.201099i	−0.0400346	−	0.0130080i	−0.328966	+	0.944342i	$0.606700\pi$
$240$		0			0
$241$	0.238703	−	1.12301i	0.0153762	−	0.0723393i	−0.969791	−	0.243939i	$-0.921560\pi$
$241$	0.238703	−	1.12301i	0.0153762	−	0.0723393i	0.985167	+	0.171600i	$0.0548936\pi$
$242$	−5.57385	−	4.51361i	−0.358300	−	0.290146i
$243$	−18.1075	−	4.85188i	−1.16159	−	0.311248i
$244$	−3.60952	+	2.62247i	−0.231076	+	0.167887i
$245$		0			0
$246$	−0.469334	−	0.340991i	−0.0299237	−	0.0217408i
$247$	−0.372623	−	0.460151i	−0.0237094	−	0.0292787i
$248$	1.56959	+	0.0822585i	0.0996688	+	0.00522342i
$249$	25.5895	+	14.7741i	1.62167	+	0.936270i
$250$		0			0
$251$		−	13.8492i		−	0.874153i	−0.899424	−	0.437076i	$-0.856014\pi$
$251$		−	13.8492i		−	0.874153i	0.899424	−	0.437076i	$-0.143986\pi$
$252$	−1.86337	+	7.14493i	−0.117381	+	0.450088i
$253$	3.22237	+	20.3452i	0.202589	+	1.27909i
$254$	−26.6865	−	2.80487i	−1.67446	−	0.175993i
$255$		0			0
$256$	−1.43165	−	13.6212i	−0.0894778	−	0.851325i
$257$	0.0943752	−	0.352213i	0.00588696	−	0.0219704i	−0.962920	−	0.269788i	$-0.913047\pi$
$257$	0.0943752	−	0.352213i	0.00588696	−	0.0219704i	0.968807	+	0.247817i	$0.0797132\pi$
$258$	8.08608	−	51.0535i	0.503417	−	3.17845i
$259$	−2.27010	−	20.2925i	−0.141057	−	1.26092i
$260$		0			0
$261$	−18.6557	+	3.96540i	−1.15476	+	0.245452i
$262$	−0.355231	−	0.547007i	−0.0219462	−	0.0337942i
$263$	16.2018	+	24.9486i	0.999045	+	1.53839i	0.833744	+	0.552151i	$0.186193\pi$
$263$	16.2018	+	24.9486i	0.999045	+	1.53839i	0.165301	+	0.986243i	$0.447141\pi$
$264$	−23.3734	+	4.96816i	−1.43853	+	0.305769i
$265$		0			0
$266$	−21.0368	+	15.5001i	−1.28985	+	0.950371i
$267$	−0.428885	+	2.70787i	−0.0262473	+	0.165719i
$268$	−0.0903576	+	0.337219i	−0.00551947	+	0.0205989i
$269$	2.16638	+	20.6117i	0.132087	+	1.25672i	0.836911	+	0.547338i	$0.184359\pi$
$269$	2.16638	+	20.6117i	0.132087	+	1.25672i	−0.704825	+	0.709381i	$0.748974\pi$
$270$		0			0
$271$	−5.57572	−	0.586032i	−0.338701	−	0.0355989i	−0.0663487	−	0.997796i	$-0.521135\pi$
$271$	−5.57572	−	0.586032i	−0.338701	−	0.0355989i	−0.272352	+	0.962198i	$0.587802\pi$
$272$	2.54792	+	16.0869i	0.154490	+	0.975413i
$273$	−0.493108	+	0.499746i	−0.0298443	+	0.0302460i
$274$		−	20.5248i		−	1.23995i
$275$		0			0
$276$	−7.76028	−	4.48040i	−0.467114	−	0.269688i
$277$	−5.90329	−	0.309378i	−0.354694	−	0.0185887i	−0.125843	−	0.992050i	$-0.540164\pi$
$277$	−5.90329	−	0.309378i	−0.354694	−	0.0185887i	−0.228851	+	0.973461i	$0.573497\pi$
$278$	−14.6717	−	18.1181i	−0.879953	−	1.08665i
$279$	2.54748	+	1.85085i	0.152514	+	0.110808i
$280$		0			0
$281$	−6.92124	+	5.02858i	−0.412887	+	0.299980i	−0.774769	−	0.632244i	$-0.782134\pi$
$281$	−6.92124	+	5.02858i	−0.412887	+	0.299980i	0.361883	+	0.932224i	$0.382134\pi$
$282$	−11.5820	−	3.10338i	−0.689697	−	0.184804i
$283$	−11.7275	−	9.49677i	−0.697130	−	0.564525i	0.213905	−	0.976855i	$-0.431382\pi$
$283$	−11.7275	−	9.49677i	−0.697130	−	0.564525i	−0.911035	+	0.412330i	$0.864715\pi$
$284$	0.131547	−	0.618878i	0.00780585	−	0.0367236i
$285$		0			0
$286$	0.587957	+	0.191039i	0.0347666	+	0.0112964i
$287$	−0.322900	+	0.126433i	−0.0190602	+	0.00746312i
$288$	6.92789	−	13.5968i	0.408230	−	0.801196i
$289$	1.19910	+	5.64132i	0.0705353	+	0.331843i
$290$		0			0
$291$	30.2551	+	6.43093i	1.77359	+	0.376988i
$292$	−0.478282	−	1.24597i	−0.0279893	−	0.0729147i
$293$	−7.80680	+	7.80680i	−0.456078	+	0.456078i	−0.897366	−	0.441288i	$-0.854522\pi$
$293$	−7.80680	+	7.80680i	−0.456078	+	0.456078i	0.441288	+	0.897366i	$0.354522\pi$
$294$	21.0380	+	22.7459i	1.22696	+	1.32657i
$295$		0			0
$296$	−1.79672	+	17.0946i	−0.104432	+	0.993605i
$297$	−14.6439	−	5.62128i	−0.849727	−	0.326180i
$298$	0.905441	−	17.2768i	0.0524508	−	1.00082i
$299$	−0.254733	−	0.441210i	−0.0147316	−	0.0255158i
$300$		0			0
$301$	−23.0990	−	20.5205i	−1.33141	−	1.18278i
$302$	−15.3591	−	30.1439i	−0.883817	−	1.73459i
$303$	−24.9109	+	20.1725i	−1.43109	+	1.15888i
$304$	27.0605	−	12.0481i	1.55203	−	0.691007i
$305$		0			0
$306$	−9.85570	+	22.1363i	−0.563413	+	1.26545i
$307$	−8.14095	−	8.14095i	−0.464628	−	0.464628i	0.435541	−	0.900169i	$-0.356557\pi$
$307$	−8.14095	−	8.14095i	−0.464628	−	0.464628i	−0.900169	+	0.435541i	$0.856557\pi$
$308$	2.28864	−	6.08338i	0.130407	−	0.346632i
$309$	−26.1655	+	8.50169i	−1.48850	+	0.483644i
$310$		0			0
$311$	−21.3562	+	19.2292i	−1.21100	+	1.09039i	−0.217556	+	0.976048i	$0.569808\pi$
$311$	−21.3562	+	19.2292i	−1.21100	+	1.09039i	−0.993442	+	0.114339i	$0.963525\pi$
$312$	0.495655	−	0.321882i	0.0280610	−	0.0182230i
$313$	−0.498133	−	9.50493i	−0.0281561	−	0.537251i	−0.975900	−	0.218218i	$-0.929975\pi$
$313$	−0.498133	−	9.50493i	−0.0281561	−	0.537251i	0.947744	−	0.319032i	$-0.103358\pi$
$314$	5.98554	−	18.4216i	0.337783	−	1.03959i
$315$		0			0
$316$	−2.98662	−	9.19189i	−0.168011	−	0.517084i
$317$	−7.28729	+	2.79733i	−0.409295	+	0.157114i	−0.554299	−	0.832317i	$-0.687014\pi$
$317$	−7.28729	+	2.79733i	−0.409295	+	0.157114i	0.145004	+	0.989431i	$0.453680\pi$
$318$	13.4728	+	50.2810i	0.755515	+	2.81962i
$319$	16.6965	−	1.75487i	0.934824	−	0.0982540i
$320$		0			0
$321$	−1.81768	+	2.50182i	−0.101453	+	0.139638i
$322$	−19.9642	+	10.3410i	−1.11256	+	0.576281i
$323$	−18.2019	+	9.27431i	−1.01278	+	0.516036i
$324$	−1.34150	+	0.774516i	−0.0745278	+	0.0430287i
$325$		0			0
$326$	−11.7489	+	20.3497i	−0.650711	+	1.12706i
$327$	6.70673	+	4.35540i	0.370883	+	0.240854i
$328$	0.288317	−	0.0456650i	0.0159197	−	0.00252143i
$329$	−5.29417	+	4.83138i	−0.291877	+	0.266362i
$330$		0			0
$331$	0.945325	+	0.420886i	0.0519597	+	0.0231340i	0.432552	−	0.901609i	$-0.357613\pi$
$331$	0.945325	+	0.420886i	0.0519597	+	0.0231340i	−0.380592	+	0.924743i	$0.624280\pi$
$332$	6.53515	−	1.75109i	0.358663	−	0.0961035i
$333$	−21.6715	+	26.7621i	−1.18759	+	1.46655i
$334$	−1.81366	+	2.01427i	−0.0992388	+	0.110216i
$335$		0			0
$336$	−17.7644	−	30.2991i	−0.969125	−	1.65295i
$337$	1.66773	+	0.849753i	0.0908472	+	0.0462890i	0.498824	−	0.866703i	$-0.333765\pi$
$337$	1.66773	+	0.849753i	0.0908472	+	0.0462890i	−0.407977	+	0.912992i	$0.633765\pi$
$338$	21.0202	−	1.10162i	1.14335	−	0.0599202i
$339$	−8.53950	−	9.48407i	−0.463802	−	0.515104i
$340$		0			0
$341$	−2.05982	−	1.85467i	−0.111545	−	0.100436i
$342$	43.5258	+	6.89381i	2.35361	+	0.372774i
$343$	18.2305	−	3.26350i	0.984352	−	0.176212i
$344$	15.2880	+	21.0421i	0.824272	+	1.13451i
$345$		0			0
$346$	0.185357	+	0.416319i	0.00996486	+	0.0223814i
$347$	−0.712508	+	1.85615i	−0.0382494	+	0.0996431i	−0.951375	−	0.308036i	$-0.900328\pi$
$347$	−0.712508	+	1.85615i	−0.0382494	+	0.0996431i	0.913125	+	0.407679i	$0.133662\pi$
$348$	−3.97762	+	6.12500i	−0.213223	+	0.328335i
$349$	4.37015			0.233929			0.116964	−	0.993136i	$-0.462684\pi$
$349$	4.37015			0.233929			0.116964	+	0.993136i	$0.462684\pi$
$350$		0			0
$351$	0.387952			0.0207073
$352$	−7.31587	+	11.2654i	−0.389937	+	0.600450i
$353$	−6.69256	+	17.4347i	−0.356209	+	0.927957i	0.632017	+	0.774955i	$0.282227\pi$
$353$	−6.69256	+	17.4347i	−0.356209	+	0.927957i	−0.988226	+	0.153002i	$0.951106\pi$
$354$	−9.29042	−	20.8666i	−0.493780	−	1.10905i
$355$		0			0
$356$	0.368984	+	0.507863i	0.0195561	+	0.0269167i
$357$	13.3280	+	20.2260i	0.705393	+	1.07047i
$358$	20.9867	+	3.32396i	1.10918	+	0.175677i
$359$	−12.4207	−	11.1836i	−0.655539	−	0.590250i	0.272761	−	0.962082i	$-0.412063\pi$
$359$	−12.4207	−	11.1836i	−0.655539	−	0.590250i	−0.928300	+	0.371832i	$0.878730\pi$
$360$		0			0
$361$	12.1464	+	13.4899i	0.639282	+	0.709995i
$362$	37.2694	−	1.95321i	1.95884	−	0.102658i
$363$	10.7735	+	5.48937i	0.565462	+	0.288117i
$364$	0.00107477	+	0.160750i	5.63332e−5	+	0.00842560i
$365$		0			0
$366$	21.1264	−	23.4633i	1.10430	−	1.22644i
$367$	6.07938	−	7.50742i	0.317341	−	0.391884i	−0.593368	−	0.804931i	$-0.702202\pi$
$367$	6.07938	−	7.50742i	0.317341	−	0.391884i	0.910710	+	0.413047i	$0.135536\pi$
$368$	24.6188	−	6.59659i	1.28334	−	0.343871i
$369$	0.534260	+	0.237868i	0.0278125	+	0.0123829i
$370$		0			0
$371$	29.6563	+	9.41718i	1.53968	+	0.488916i
$372$	1.19091	−	0.188622i	0.0617459	−	0.00977959i
$373$	4.12458	+	2.67853i	0.213563	+	0.138689i	0.646988	−	0.762500i	$-0.276028\pi$
$373$	4.12458	+	2.67853i	0.213563	+	0.138689i	−0.433425	+	0.901190i	$0.642695\pi$
$374$	10.6647	−	18.4717i	0.551456	−	0.955150i
$375$		0			0
$376$	5.22511	−	3.01672i	0.269465	−	0.155575i
$377$	−0.369967	+	0.188508i	−0.0190543	+	0.00970865i
$378$	0.781708	−	17.1030i	0.0402067	−	0.879686i
$379$	7.39900	−	10.1839i	0.380061	−	0.523109i	−0.575540	−	0.817774i	$-0.695208\pi$
$379$	7.39900	−	10.1839i	0.380061	−	0.523109i	0.955601	+	0.294665i	$0.0952079\pi$
$380$		0			0
$381$	44.9900	−	4.72864i	2.30491	−	0.242255i
$382$	1.69690	+	6.33292i	0.0868210	+	0.324020i
$383$	16.7403	−	6.42601i	0.855391	−	0.328354i	0.109146	−	0.994026i	$-0.465188\pi$
$383$	16.7403	−	6.42601i	0.855391	−	0.328354i	0.746245	+	0.665672i	$0.231855\pi$
$384$	11.4883	+	35.3574i	0.586260	+	1.80432i
$385$		0			0
$386$	−1.53944	+	4.73792i	−0.0783556	+	0.241154i
$387$	2.72712	+	52.0365i	0.138627	+	2.64516i
$388$	5.93974	−	3.85731i	0.301544	−	0.195825i
$389$	−8.86329	+	7.98055i	−0.449387	+	0.404630i	−0.862506	−	0.506047i	$-0.831106\pi$
$389$	−8.86329	+	7.98055i	−0.449387	+	0.404630i	0.413119	+	0.910677i	$0.364439\pi$
$390$		0			0
$391$	−16.7170	+	5.43168i	−0.845415	+	0.274692i
$392$	−15.5785	−	0.607684i	−0.786832	−	0.0306927i
$393$	0.777518	+	0.777518i	0.0392206	+	0.0392206i
$394$	8.31153	−	18.6680i	0.418729	−	0.940480i
$395$		0			0
$396$	−10.0138	+	4.45844i	−0.503213	+	0.224045i
$397$	−29.1590	+	23.6125i	−1.46345	+	1.18508i	−0.519732	+	0.854329i	$0.673968\pi$
$397$	−29.1590	+	23.6125i	−1.46345	+	1.18508i	−0.943719	+	0.330750i	$0.892698\pi$
$398$	3.19987	+	6.28010i	0.160395	+	0.314793i
$399$	29.2573	−	32.9337i	1.46470	−	1.64875i
$400$		0			0
$401$	0.106730	+	0.184861i	0.00532982	+	0.00923152i	0.868678	−	0.495377i	$-0.164970\pi$
$401$	0.106730	+	0.184861i	0.00532982	+	0.00923152i	−0.863348	+	0.504609i	$0.831637\pi$
$402$	0.129298	−	2.46715i	0.00644879	−	0.123050i
$403$	0.0639999	+	0.0245673i	0.00318806	+	0.00122378i
$404$	−0.767189	+	7.29932i	−0.0381691	+	0.363155i
$405$		0			0
$406$	7.56499	+	16.6900i	0.375444	+	0.828313i
$407$	21.4341	−	21.4341i	1.06245	−	1.06245i
$408$	−7.30726	−	19.0361i	−0.361763	−	0.942426i
$409$	31.2443	+	6.64117i	1.54493	+	0.328385i	0.900011	−	0.435867i	$-0.143558\pi$
$409$	31.2443	+	6.64117i	1.54493	+	0.328385i	0.644918	+	0.764252i	$0.276891\pi$
$410$		0			0
$411$	7.19417	+	33.8459i	0.354862	+	1.66950i
$412$	−2.85990	+	5.61287i	−0.140897	+	0.276526i
$413$	−13.4992	−	2.04565i	−0.664255	−	0.100660i
$414$	36.0620	+	11.7173i	1.77235	+	0.575872i
$415$		0			0
$416$	0.0690729	−	0.324962i	0.00338658	−	0.0159326i
$417$	30.5447	+	24.7346i	1.49578	+	1.21126i
$418$	−37.4691	−	10.0398i	−1.83267	−	0.491063i
$419$	−8.57555	+	6.23050i	−0.418943	+	0.304380i	−0.777212	−	0.629238i	$-0.783367\pi$
$419$	−8.57555	+	6.23050i	−0.418943	+	0.304380i	0.358269	+	0.933618i	$0.383367\pi$
$420$		0			0
$421$	7.12732	+	5.17830i	0.347364	+	0.252375i	0.747762	−	0.663966i	$-0.231128\pi$
$421$	7.12732	+	5.17830i	0.347364	+	0.252375i	−0.400398	+	0.916341i	$0.631128\pi$
$422$	6.79723	+	8.39388i	0.330884	+	0.408608i
$423$	12.0710	+	0.632612i	0.586910	+	0.0307586i
$424$	−22.6839	−	13.0965i	−1.10163	−	0.636024i
$425$		0			0
$426$			4.47737i			0.216929i
$427$	−5.00637	−	18.1965i	−0.242275	−	0.880591i
$428$	0.110767	+	0.699356i	0.00535413	+	0.0338047i
$429$	−1.03652	−	0.108943i	−0.0500436	−	0.00525980i
$430$		0			0
$431$	−0.640581	−	6.09472i	−0.0308557	−	0.293572i	−0.999058	−	0.0434025i	$-0.986180\pi$
$431$	−0.640581	−	6.09472i	−0.0308557	−	0.293572i	0.968202	−	0.250170i	$-0.0804864\pi$
$432$	−5.02322	+	18.7469i	−0.241680	+	0.901961i
$433$	−5.58866	+	35.2854i	−0.268574	+	1.69571i	0.372339	+	0.928097i	$0.378556\pi$
$433$	−5.58866	+	35.2854i	−0.268574	+	1.69571i	−0.640913	+	0.767613i	$0.721444\pi$
$434$	1.21202	−	2.77197i	0.0581787	−	0.133059i
$435$		0			0
$436$	1.79104	−	0.380697i	0.0857751	−	0.0182321i
$437$	17.4106	+	26.8100i	0.832861	+	1.28249i
$438$	5.14383	+	7.92080i	0.245782	+	0.378470i
$439$	−25.5065	+	5.42157i	−1.21736	+	0.258757i	−0.771431	−	0.636312i	$-0.780459\pi$
$439$	−25.5065	+	5.42157i	−1.21736	+	0.258757i	−0.445926	+	0.895070i	$0.647126\pi$
$440$		0			0
$441$	−25.5120	−	18.0194i	−1.21486	−	0.858064i
$442$	−0.0825241	+	0.521037i	−0.00392527	+	0.0247832i
$443$	8.76626	−	32.7161i	0.416498	−	1.55439i	−0.365319	−	0.930882i	$-0.619040\pi$
$443$	8.76626	−	32.7161i	0.416498	−	1.55439i	0.781817	−	0.623508i	$-0.214293\pi$
$444$	1.37835	+	13.1141i	0.0654135	+	0.622368i
$445$		0			0
$446$	24.8335	+	2.61010i	1.17590	+	0.123592i
$447$	4.56264	+	28.8074i	0.215805	+	1.36254i
$448$	10.6960	+	2.78948i	0.505340	+	0.131791i
$449$		−	17.8247i		−	0.841199i	−0.907246	−	0.420600i	$-0.861820\pi$
$449$		−	17.8247i		−	0.841199i	0.907246	−	0.420600i	$-0.138180\pi$
$450$		0			0
$451$	−0.445816	−	0.257392i	−0.0209927	−	0.0121201i
$452$	−2.91814	−	0.152933i	−0.137258	−	0.00719338i
$453$	35.8934	+	44.3247i	1.68642	+	2.08255i
$454$	−17.3691	−	12.6194i	−0.815173	−	0.592258i
$455$		0			0
$456$	−30.0010	+	21.7970i	−1.40493	+	1.02074i
$457$	−8.24133	−	2.20826i	−0.385513	−	0.103298i	0.0608568	−	0.998147i	$-0.480617\pi$
$457$	−8.24133	−	2.20826i	−0.385513	−	0.103298i	−0.446370	+	0.894849i	$0.647283\pi$
$458$	−5.22289	−	4.22941i	−0.244050	−	0.197627i
$459$	2.78288	−	13.0924i	0.129893	−	0.611101i
$460$		0			0
$461$	25.2246	+	8.19596i	1.17483	+	0.381724i	0.830442	−	0.557105i	$-0.188088\pi$
$461$	25.2246	+	8.19596i	1.17483	+	0.381724i	0.344384	+	0.938829i	$0.388088\pi$
$462$	−6.89134	+	45.4760i	−0.320614	+	2.11573i
$463$	10.3899	−	20.3912i	0.482857	−	0.947661i	−0.513142	−	0.858304i	$-0.671519\pi$
$463$	10.3899	−	20.3912i	0.482857	−	0.947661i	0.996000	−	0.0893575i	$-0.0284814\pi$
$464$	−4.31887	−	20.3187i	−0.200498	−	0.943271i
$465$		0			0
$466$	40.8410	+	8.68102i	1.89192	+	0.402140i
$467$	−3.19548	−	8.32450i	−0.147869	−	0.385212i	0.839562	−	0.543264i	$-0.182812\pi$
$467$	−3.19548	−	8.32450i	−0.147869	−	0.385212i	−0.987431	+	0.158052i	$0.949479\pi$
$468$	0.191702	−	0.191702i	0.00886142	−	0.00886142i
$469$	−1.20050	−	0.860009i	−0.0554338	−	0.0397115i
$470$		0			0
$471$	−3.41334	+	32.4757i	−0.157278	+	1.49640i
$472$	10.7300	+	4.11886i	0.493888	+	0.189586i
$473$	2.40053	−	45.8047i	0.110376	−	2.10610i
$474$	34.1972	+	59.2314i	1.57073	+	2.72059i
$475$		0			0
$476$	5.43263	+	1.11683i	0.249004	+	0.0511899i
$477$	−23.8235	−	46.7562i	−1.09080	−	2.14082i
$478$	0.819472	−	0.663596i	0.0374818	−	0.0303522i
$479$	−2.18656	+	0.973518i	−0.0999064	+	0.0444812i	−0.456081	−	0.889938i	$-0.650747\pi$
$479$	−2.18656	+	0.973518i	−0.0999064	+	0.0444812i	0.356175	+	0.934419i	$0.384081\pi$
$480$		0			0
$481$	−0.304934	+	0.684892i	−0.0139038	+	0.0312284i
$482$	1.31543	+	1.31543i	0.0599161	+	0.0599161i
$483$	29.2970	−	24.0503i	1.33306	−	1.09433i
$484$	2.63308	−	0.855538i	0.119685	−	0.0388881i
$485$		0			0
$486$	22.5731	−	20.3249i	1.02394	−	0.921957i
$487$	4.06415	−	2.63929i	0.184164	−	0.119598i	−0.449264	−	0.893399i	$-0.648314\pi$
$487$	4.06415	−	2.63929i	0.184164	−	0.119598i	0.633428	+	0.773801i	$0.281647\pi$
$488$	0.831460	+	15.8652i	0.0376384	+	0.718184i
$489$	12.2414	−	37.6753i	0.553577	−	1.70374i
$490$		0			0
$491$	−9.20020	−	28.3153i	−0.415199	−	1.27785i	−0.912073	−	0.410029i	$-0.865519\pi$
$491$	−9.20020	−	28.3153i	−0.415199	−	1.27785i	0.496874	−	0.867823i	$-0.334481\pi$
$492$	0.209065	−	0.0802525i	0.00942537	−	0.00361806i
$493$	3.70780	+	13.8377i	0.166991	+	0.623218i
$494$	0.954148	−	0.100285i	0.0429291	−	0.00451203i
$495$		0			0
$496$	−2.01583	+	2.77456i	−0.0905136	+	0.124581i
$497$	2.25426	+	1.44260i	0.101117	+	0.0647094i
$498$	−42.6595	+	21.7361i	−1.91162	+	0.974018i
$499$	−33.6862	+	19.4488i	−1.50800	+	0.870646i	−0.508046	+	0.861330i	$0.669632\pi$
$499$	−33.6862	+	19.4488i	−1.50800	+	0.870646i	−0.999957	+	0.00931623i	$0.997035\pi$
$500$		0			0
$501$	2.28474	−	3.95729i	0.102075	−	0.176799i
$502$	18.8200	+	12.2218i	0.839977	+	0.545488i
$503$	−37.4880	+	5.93752i	−1.67151	+	0.264741i	−0.919120	−	0.393979i	$-0.871098\pi$
$503$	−37.4880	+	5.93752i	−1.67151	+	0.264741i	−0.752389	+	0.658719i	$0.771098\pi$
$504$	17.7235	+	19.4212i	0.789467	+	0.865090i
$505$		0			0
$506$	−30.4914	−	13.5756i	−1.35551	−	0.603510i
$507$	−34.2767	+	9.18442i	−1.52228	+	0.407894i
$508$	6.51859	−	8.04979i	0.289216	−	0.357152i
$509$	−6.94597	+	7.71429i	−0.307875	+	0.341930i	−0.877149	−	0.480218i	$-0.840558\pi$
$509$	−6.94597	+	7.71429i	−0.307875	+	0.341930i	0.569274	+	0.822148i	$0.307224\pi$
$510$		0			0
$511$	5.64528	−	0.0377441i	0.249733	−	0.00166970i
$512$	−4.47894	−	2.28214i	−0.197943	−	0.100857i
$513$	−24.3093	+	1.27400i	−1.07328	+	0.0562483i
$514$	0.395345	+	0.439075i	0.0174379	+	0.0193668i
$515$		0			0
$516$	14.8280	+	13.3512i	0.652768	+	0.587755i
$517$	−10.5090	−	1.66446i	−0.462184	−	0.0732027i
$518$	29.5794	+	14.8232i	1.29964	+	0.651293i
$519$	−0.451584	−	0.621552i	−0.0198223	−	0.0272831i
$520$		0			0
$521$	−4.89041	−	10.9840i	−0.214253	−	0.481219i	0.774164	−	0.632985i	$-0.218171\pi$
$521$	−4.89041	−	10.9840i	−0.214253	−	0.481219i	−0.988416	+	0.151766i	$0.951504\pi$
$522$	11.0749	−	28.8512i	0.484737	−	1.26278i
$523$	13.0588	−	20.1088i	0.571023	−	0.879298i	−0.428685	−	0.903454i	$-0.641023\pi$
$523$	13.0588	−	20.1088i	0.571023	−	0.879298i	0.999708	+	0.0241556i	$0.00768970\pi$
$524$	0.251771			0.0109987
$525$		0			0
$526$	−48.2012			−2.10167
$527$	1.28817	−	1.98361i	0.0561136	−	0.0864074i
$528$	18.6853	−	48.6769i	0.813175	−	2.11839i
$529$	1.83261	+	4.11611i	0.0796787	+	0.178961i
$530$		0			0
$531$	13.5344	+	18.6285i	0.587342	+	0.808407i
$532$	−0.595233	−	10.0692i	−0.0258066	−	0.436554i
$533$	0.0125753	+	0.00199173i	0.000544695	+	8.62712e-5i
$534$	−3.30130	−	2.97251i	−0.142861	−	0.128633i
$535$		0			0
$536$	0.831817	+	0.923827i	0.0359290	+	0.0399032i
$537$	−35.7727	+	1.87477i	−1.54370	+	0.0809021i
$538$	−29.9216	−	15.2458i	−1.29001	−	0.657294i
$539$	20.6758	+	18.1219i	0.890570	+	0.780565i
$540$		0			0
$541$	−12.8091	+	14.2259i	−0.550705	+	0.611620i	−0.952659	−	0.304040i	$-0.901664\pi$
$541$	−12.8091	+	14.2259i	−0.550705	+	0.611620i	0.401954	+	0.915660i	$0.368331\pi$
$542$	5.71693	−	7.05982i	0.245563	−	0.303245i
$543$	−60.7737	+	16.2843i	−2.60805	+	0.698825i
$544$	−10.4712	−	4.66208i	−0.448949	−	0.199885i
$545$		0			0
$546$	−0.243952	−	1.11112i	−0.0104402	−	0.0475516i
$547$	12.3236	−	1.95187i	0.526919	−	0.0834558i	0.112693	−	0.993630i	$-0.464052\pi$
$547$	12.3236	−	1.95187i	0.526919	−	0.0834558i	0.414226	+	0.910174i	$0.364052\pi$
$548$	6.64468	+	4.31510i	0.283847	+	0.184332i
$549$	−15.9141	+	27.5641i	−0.679199	+	1.17641i
$550$		0			0
$551$	22.5633	−	13.0269i	0.961230	−	0.554967i
$552$	−28.4300	+	14.4858i	−1.21006	+	0.616556i
$553$	40.8400	+	1.86663i	1.73669	+	0.0793770i
$554$	5.63005	−	7.74910i	0.239198	−	0.329228i
$555$		0			0
$556$	8.95012	−	0.940695i	0.379570	−	0.0398944i
$557$	5.89390	+	21.9963i	0.249732	+	0.932014i	0.970946	+	0.239301i	$0.0769182\pi$
$557$	5.89390	+	21.9963i	0.249732	+	0.932014i	−0.721213	+	0.692713i	$0.756415\pi$
$558$	−4.76331	+	1.82846i	−0.201647	+	0.0774050i
$559$	0.350558	+	1.07891i	0.0148270	+	0.0456329i
$560$		0			0
$561$	−11.1118	+	34.1985i	−0.469139	+	1.44386i
$562$	−0.725488	−	13.8431i	−0.0306029	−	0.583937i
$563$	24.4754	−	15.8945i	1.03152	−	0.669874i	0.0862825	−	0.996271i	$-0.472501\pi$
$563$	24.4754	−	15.8945i	1.03152	−	0.669874i	0.945233	+	0.326397i	$0.105835\pi$
$564$	3.43967	−	3.09710i	0.144836	−	0.130411i
$565$		0			0
$566$	23.2549	−	7.55597i	0.977476	−	0.317601i
$567$	−1.06827	−	6.46474i	−0.0448631	−	0.271494i
$568$	−1.59307	−	1.59307i	−0.0668436	−	0.0668436i
$569$	0.645950	−	1.45083i	0.0270796	−	0.0608218i	−0.899499	−	0.436922i	$-0.856069\pi$
$569$	0.645950	−	1.45083i	0.0270796	−	0.0608218i	0.926579	+	0.376100i	$0.122735\pi$
$570$		0			0
$571$	3.28341	−	1.46187i	0.137406	−	0.0611773i	−0.336882	−	0.941547i	$-0.609372\pi$
$571$	3.28341	−	1.46187i	0.137406	−	0.0611773i	0.474288	+	0.880370i	$0.342706\pi$
$572$	−0.185458	+	0.150181i	−0.00775441	+	0.00627940i
$573$	−5.01800	−	9.84838i	−0.209630	−	0.411422i
$574$	0.113145	−	0.550374i	0.00472258	−	0.0229722i
$575$		0			0
$576$	−9.32098	−	16.1444i	−0.388374	−	0.672683i
$577$	1.16904	−	22.3066i	0.0486677	−	0.928634i	−0.859788	−	0.510652i	$-0.829404\pi$
$577$	1.16904	−	22.3066i	0.0486677	−	0.928634i	0.908455	−	0.417982i	$-0.137263\pi$
$578$	−8.72433	−	3.34896i	−0.362884	−	0.139298i
$579$	0.877889	−	8.35256i	0.0364838	−	0.347121i
$580$		0			0
$581$	−2.80113	+	28.4815i	−0.116210	+	1.18161i
$582$	−35.4392	+	35.4392i	−1.46900	+	1.46900i
$583$	16.5535	+	43.1234i	0.685577	+	1.78599i
$584$	−4.64845	−	0.988058i	−0.192354	−	0.0408861i
$585$		0			0
$586$	−3.71938	−	17.4983i	−0.153646	−	0.722848i
$587$	19.7026	−	38.6684i	0.813211	−	1.59602i	0.0102788	−	0.999947i	$-0.496728\pi$
$587$	19.7026	−	38.6684i	0.813211	−	1.59602i	0.802933	−	0.596070i	$-0.203272\pi$
$588$	−11.7868	+	2.02875i	−0.486078	+	0.0836644i
$589$	−4.09095	−	1.32923i	−0.168565	−	0.0547699i
$590$		0			0
$591$	−7.16259	+	33.6973i	−0.294630	+	1.38612i
$592$	−29.1476	−	23.6033i	−1.19796	−	0.970088i
$593$	12.4912	+	3.34701i	0.512953	+	0.137445i	0.506005	−	0.862531i	$-0.331122\pi$
$593$	12.4912	+	3.34701i	0.512953	+	0.137445i	0.00694789	+	0.999976i	$0.497788\pi$
$594$	20.5621	−	14.9392i	0.843673	−	0.612964i
$595$		0			0
$596$	5.40284	+	3.92539i	0.221309	+	0.160790i
$597$	−7.47793	−	9.23448i	−0.306051	−	0.377942i
$598$	0.824371	+	0.0432035i	0.0337110	+	0.00176672i
$599$	19.9444	+	11.5149i	0.814905	+	0.470485i	0.848656	−	0.528945i	$-0.177412\pi$
$599$	19.9444	+	11.5149i	0.814905	+	0.470485i	−0.0337516	+	0.999430i	$0.510745\pi$
$600$		0			0
$601$			14.0409i			0.572740i	0.958119	+	0.286370i	$0.0924486\pi$
$601$			14.0409i			0.572740i	−0.958119	+	0.286370i	$0.907551\pi$
$602$	48.2705	−	13.2806i	1.96736	−	0.541276i
$603$	0.389602	+	2.45985i	0.0158658	+	0.100173i
$604$	12.9879	+	1.36508i	0.528469	+	0.0555443i
$605$		0			0
$606$	−5.42907	−	51.6542i	−0.220541	−	2.09831i
$607$	−10.2468	+	38.2415i	−0.415904	+	1.55218i	0.367113	+	0.930176i	$0.380346\pi$
$607$	−10.2468	+	38.2415i	−0.415904	+	1.55218i	−0.783017	+	0.622000i	$0.786320\pi$
$608$	−3.26100	+	20.5892i	−0.132251	+	0.835001i
$609$	−18.3249	−	24.8707i	−0.742564	−	1.00781i
$610$		0			0
$611$	0.257404	−	0.0547130i	0.0104135	−	0.00221345i
$612$	−5.09433	−	7.84459i	−0.205926	−	0.317099i
$613$	−2.11361	−	3.25467i	−0.0853679	−	0.131455i	0.793407	−	0.608691i	$-0.208305\pi$
$613$	−2.11361	−	3.25467i	−0.0853679	−	0.131455i	−0.878775	+	0.477236i	$0.841639\pi$
$614$	18.2473	−	3.87858i	0.736400	−	0.156527i
$615$		0			0
$616$	−13.7286	−	18.6325i	−0.553140	−	0.750725i
$617$	4.36290	−	27.5463i	0.175644	−	1.10897i	−0.729536	−	0.683943i	$-0.760264\pi$
$617$	4.36290	−	27.5463i	0.175644	−	1.10897i	0.905180	−	0.425029i	$-0.139736\pi$
$618$	11.5378	−	43.0597i	0.464118	−	1.73211i
$619$	−2.82187	−	26.8483i	−0.113421	−	1.07913i	−0.892142	−	0.451755i	$-0.850798\pi$
$619$	−2.82187	−	26.8483i	−0.113421	−	1.07913i	0.778721	−	0.627370i	$-0.215869\pi$
$620$		0			0
$621$	−20.8305	−	2.18937i	−0.835898	−	0.0878564i
$622$	−7.28427	−	45.9911i	−0.292073	−	1.84408i
$623$	−2.56027	+	0.704401i	−0.102575	+	0.0282212i
$624$			1.28957i			0.0516239i
$625$		0			0
$626$	13.3561	+	7.71114i	0.533816	+	0.308199i
$627$	65.3067	+	3.42258i	2.60810	+	0.136685i
$628$	4.70541	+	5.81069i	0.187766	+	0.231872i
$629$	20.9260	+	15.2037i	0.834376	+	0.606209i
$630$		0			0
$631$	8.70119	−	6.32178i	0.346389	−	0.251666i	−0.400964	−	0.916094i	$-0.631325\pi$
$631$	8.70119	−	6.32178i	0.346389	−	0.251666i	0.747353	+	0.664428i	$0.231325\pi$
$632$	−33.2423	−	8.90724i	−1.32231	−	0.354311i
$633$	−14.1510	−	11.4592i	−0.562451	−	0.455464i
$634$	2.62964	−	12.3715i	0.104436	−	0.491335i
$635$		0			0
$636$	−19.1105	−	6.20937i	−0.757780	−	0.246217i
$637$	−0.638026	−	0.235176i	−0.0252795	−	0.00931801i
$638$	−12.3498	+	24.2379i	−0.488935	+	0.959589i
$639$	−0.938426	−	4.41495i	−0.0371236	−	0.174653i
$640$		0			0
$641$	−29.4673	−	6.26346i	−1.16389	−	0.247392i	−0.414831	−	0.909898i	$-0.636159\pi$
$641$	−29.4673	−	6.26346i	−1.16389	−	0.247392i	−0.749056	+	0.662506i	$0.769493\pi$
$642$	−1.79569	−	4.67792i	−0.0708701	−	0.184623i
$643$	20.4056	−	20.4056i	0.804720	−	0.804720i	−0.179110	−	0.983829i	$-0.557322\pi$
$643$	20.4056	−	20.4056i	0.804720	−	0.804720i	0.983829	+	0.179110i	$0.0573217\pi$
$644$	0.849471	−	8.63730i	0.0334739	−	0.340357i
$645$		0			0
$646$	3.45998	−	32.9195i	0.136131	−	1.29520i
$647$	17.8718	+	6.86034i	0.702613	+	0.269708i	0.683334	−	0.730106i	$-0.260529\pi$
$647$	17.8718	+	6.86034i	0.702613	+	0.269708i	0.0192794	+	0.999814i	$0.493863\pi$
$648$	−0.288675	+	5.50825i	−0.0113402	+	0.216384i
$649$	−10.1343	−	17.5531i	−0.397805	−	0.689019i
$650$		0			0
$651$	−1.02704	+	4.99588i	−0.0402531	+	0.195804i
$652$	−4.11792	−	8.08188i	−0.161270	−	0.316511i
$653$	−9.38043	+	7.59612i	−0.367084	+	0.297259i	−0.795060	−	0.606531i	$-0.792560\pi$
$653$	−9.38043	+	7.59612i	−0.367084	+	0.297259i	0.427975	+	0.903791i	$0.359227\pi$
$654$	−11.8373	+	5.27031i	−0.462876	+	0.206086i
$655$		0			0
$656$	−0.259071	+	0.581883i	−0.0101150	+	0.0227187i
$657$	−6.73225	−	6.73225i	−0.262650	−	0.262650i
$658$	−1.89339	−	11.4580i	−0.0738120	−	0.446681i
$659$	15.5052	−	5.03793i	0.603995	−	0.196250i	0.00897383	−	0.999960i	$-0.497144\pi$
$659$	15.5052	−	5.03793i	0.603995	−	0.196250i	0.595022	+	0.803710i	$0.297144\pi$
$660$		0			0
$661$	10.4225	−	9.38450i	0.405390	−	0.365015i	−0.441065	−	0.897475i	$-0.645399\pi$
$661$	10.4225	−	9.38450i	0.405390	−	0.365015i	0.846455	+	0.532460i	$0.178732\pi$
$662$	−1.40620	+	0.913195i	−0.0546534	+	0.0354923i
$663$	−0.0465449	−	0.888130i	−0.00180766	−	0.0344921i
$664$	7.44463	−	22.9122i	0.288908	−	0.889166i
$665$		0			0
$666$	−17.2426	−	53.0674i	−0.668138	−	2.05632i
$667$	20.9287	−	8.03376i	0.810361	−	0.311069i
$668$	−0.270798	−	1.01063i	−0.0104775	−	0.0391025i
$669$	−41.8660	+	4.40029i	−1.61863	+	0.170125i
$670$		0			0
$671$	16.4678	−	22.6659i	0.635731	−	0.875008i
$672$	24.6916	+	1.12855i	0.952498	+	0.0435347i
$673$	0.252552	−	0.128682i	0.00973515	−	0.00496031i	−0.449116	−	0.893473i	$-0.648261\pi$
$673$	0.252552	−	0.128682i	0.00973515	−	0.00496031i	0.458851	+	0.888513i	$0.348261\pi$
$674$	−2.62652	+	1.51642i	−0.101170	+	0.0584103i
$675$		0			0
$676$	−4.06262	+	7.03667i	−0.156255	+	0.270641i
$677$	28.0912	+	18.2427i	1.07963	+	0.701123i	0.956637	−	0.291284i	$-0.0940825\pi$
$677$	28.0912	+	18.2427i	1.07963	+	0.701123i	0.122998	+	0.992407i	$0.460749\pi$
$678$	20.4242	−	3.23488i	0.784387	−	0.124235i
$679$	6.42445	+	29.2613i	0.246548	+	1.12295i
$680$		0			0
$681$	33.0654	+	14.7217i	1.26707	+	0.564136i
$682$	4.33814	−	1.16240i	0.166116	−	0.0445106i
$683$	14.2385	−	17.5831i	0.544821	−	0.672798i	−0.428155	−	0.903706i	$-0.640836\pi$
$683$	14.2385	−	17.5831i	0.544821	−	0.672798i	0.972976	+	0.230907i	$0.0741694\pi$
$684$	−11.3826	+	12.6417i	−0.435225	+	0.483367i
$685$		0			0
$686$	−11.6535	+	27.6538i	−0.444931	+	1.05583i
$687$	10.0951	+	5.14374i	0.385154	+	0.196246i
$688$	−56.6749	+	2.97020i	−2.16071	+	0.113238i
$689$	−0.764441	−	0.848997i	−0.0291229	−	0.0323442i
$690$		0			0
$691$	21.1493	+	19.0429i	0.804557	+	0.724427i	0.964895	−	0.262636i	$-0.0845917\pi$
$691$	21.1493	+	19.0429i	0.804557	+	0.724427i	−0.160338	+	0.987062i	$0.551258\pi$
$692$	−0.173748	−	0.0275190i	−0.00660492	−	0.00104612i
$693$	−2.73619	−	46.2863i	−0.103939	−	1.75827i
$694$	−1.89358	−	2.60628i	−0.0718792	−	0.0989332i
$695$		0			0
$696$	10.5773	+	23.7571i	0.400933	+	0.900511i
$697$	0.157421	−	0.410097i	0.00596276	−	0.0155335i
$698$	−3.85664	+	5.93870i	−0.145976	+	0.224783i
$699$	−70.3907			−2.66242
$700$		0			0
$701$	29.7376			1.12317			0.561587	−	0.827418i	$-0.310191\pi$
$701$	29.7376			1.12317			0.561587	+	0.827418i	$0.310191\pi$
$702$	−0.342366	+	0.527197i	−0.0129218	+	0.0198978i
$703$	16.8582	−	43.9171i	0.635819	−	1.65637i
$704$	6.67433	+	14.9908i	0.251548	+	0.564986i
$705$		0			0
$706$	−17.7863	−	24.4807i	−0.669396	−	0.921345i
$707$	−27.7560	−	13.9094i	−1.04387	−	0.523118i
$708$	8.70856	+	1.37930i	0.327288	+	0.0518373i
$709$	−6.43362	−	5.79286i	−0.241620	−	0.217555i	0.539420	−	0.842037i	$-0.318644\pi$
$709$	−6.43362	−	5.79286i	−0.241620	−	0.217555i	−0.781039	+	0.624482i	$0.785310\pi$
$710$		0			0
$711$	−46.1349	−	51.2380i	−1.73020	−	1.92158i
$712$	2.23225	−	0.116987i	0.0836570	−	0.00438428i
$713$	−3.29773	−	1.68028i	−0.123501	−	0.0629269i
$714$	−39.2475	+	0.262407i	−1.46880	+	0.00982033i
$715$		0			0
$716$	−5.48831	+	6.09539i	−0.205108	+	0.227795i
$717$	−1.11873	+	1.38152i	−0.0417799	+	0.0515939i
$718$	26.1589	−	7.00926i	0.976242	−	0.261583i
$719$	−24.7026	−	10.9983i	−0.921251	−	0.410167i	−0.109377	−	0.994000i	$-0.534886\pi$
$719$	−24.7026	−	10.9983i	−0.921251	−	0.410167i	−0.811874	+	0.583833i	$0.801552\pi$
$720$		0			0
$721$	−17.9622	−	19.6828i	−0.668946	−	0.733024i
$722$	−29.0509	+	4.60121i	−1.08116	+	0.171239i
$723$	−2.63025	−	1.70811i	−0.0978201	−	0.0635251i
$724$	−7.20316	+	12.4762i	−0.267703	+	0.463676i
$725$		0			0
$726$	−16.9672	+	9.79602i	−0.629712	+	0.363565i
$727$	−15.5218	+	7.90873i	−0.575670	+	0.293318i	−0.717484	−	0.696575i	$-0.754706\pi$
$727$	−15.5218	+	7.90873i	−0.575670	+	0.293318i	0.141814	+	0.989893i	$0.454706\pi$
$728$	0.482140	+	0.308542i	0.0178693	+	0.0114353i
$729$	−25.7325	+	35.4177i	−0.953055	+	1.31177i
$730$		0			0
$731$	38.9251	−	4.09119i	1.43970	−	0.151318i
$732$	3.15439	+	11.7724i	0.116590	+	0.435119i
$733$	−42.8618	+	16.4531i	−1.58314	+	0.607709i	−0.981568	−	0.191113i	$-0.938790\pi$
$733$	−42.8618	+	16.4531i	−1.58314	+	0.607709i	−0.601567	+	0.798822i	$0.705457\pi$
$734$	4.83698	+	14.8867i	0.178536	+	0.549477i
$735$		0			0
$736$	−5.54266	+	17.0586i	−0.204305	+	0.628787i
$737$	−0.114734	−	2.18925i	−0.00422628	−	0.0806422i
$738$	−0.794727	+	0.516102i	−0.0292543	+	0.0189980i
$739$	−18.2915	+	16.4697i	−0.672864	+	0.605849i	−0.933066	−	0.359705i	$-0.882877\pi$
$739$	−18.2915	+	16.4697i	−0.672864	+	0.605849i	0.260202	+	0.965554i	$0.416211\pi$
$740$		0			0
$741$	−1.53827	+	0.499813i	−0.0565096	+	0.0183611i
$742$	−38.9688	+	31.9901i	−1.43059	+	1.17439i
$743$	10.2323	+	10.2323i	0.375388	+	0.375388i	0.869435	−	0.494047i	$-0.164483\pi$
$743$	10.2323	+	10.2323i	0.375388	+	0.375388i	−0.494047	+	0.869435i	$0.664483\pi$
$744$	1.74631	−	3.92228i	0.0640229	−	0.143798i
$745$		0			0
$746$	−7.27985	+	3.24120i	−0.266534	+	0.118669i
$747$	37.5090	−	30.3742i	1.37238	−	1.11133i
$748$	3.73790	+	7.33605i	0.136671	+	0.268233i
$749$	−2.93380	−	0.603126i	−0.107199	−	0.0220377i
$750$		0			0
$751$	5.60583	+	9.70959i	0.204560	+	0.354308i	0.949992	−	0.312273i	$-0.101090\pi$
$751$	5.60583	+	9.70959i	0.204560	+	0.354308i	−0.745433	+	0.666581i	$0.767757\pi$
$752$	−0.689001	+	13.1469i	−0.0251253	+	0.479419i
$753$	−35.3186	−	13.5575i	−1.28708	−	0.494064i
$754$	0.0703268	−	0.669115i	0.00256115	−	0.0243677i
$755$		0			0
$756$	5.37259	+	3.84880i	0.195399	+	0.139979i
$757$	34.2009	−	34.2009i	1.24305	−	1.24305i	0.284326	−	0.958728i	$-0.408230\pi$
$757$	34.2009	−	34.2009i	1.24305	−	1.24305i	0.958728	−	0.284326i	$-0.0917697\pi$
$758$	7.30949	+	19.0419i	0.265493	+	0.691632i
$759$	55.0395	+	11.6990i	1.99781	+	0.424647i
$760$		0			0
$761$	−3.57175	−	16.8038i	−0.129476	−	0.609135i	−0.994260	−	0.106992i	$-0.965878\pi$
$761$	−3.57175	−	16.8038i	−0.129476	−	0.609135i	0.864784	−	0.502144i	$-0.167455\pi$
$762$	−33.2776	+	65.3109i	−1.20552	+	2.36597i
$763$	−1.16047	+	7.65792i	−0.0420117	+	0.277235i
$764$	−2.40697	−	0.782073i	−0.0870812	−	0.0282944i
$765$		0			0
$766$	−6.04081	+	28.4198i	−0.218263	+	1.02685i
$767$	0.389580	+	0.315476i	0.0140669	+	0.0113912i
$768$	−36.1387	−	9.68333i	−1.30404	−	0.349417i
$769$	15.2142	−	11.0538i	0.548638	−	0.398609i	−0.278645	−	0.960394i	$-0.589885\pi$
$769$	15.2142	−	11.0538i	0.548638	−	0.398609i	0.827283	+	0.561785i	$0.189885\pi$
$770$		0			0
$771$	−0.805836	−	0.585474i	−0.0290215	−	0.0210853i
$772$	−1.21020	−	1.49448i	−0.0435561	−	0.0537873i
$773$	−32.2701	−	1.69120i	−1.16067	−	0.0608283i	−0.537745	−	0.843107i	$-0.680724\pi$
$773$	−32.2701	−	1.69120i	−1.16067	−	0.0608283i	−0.622928	+	0.782279i	$0.714057\pi$
$774$	−73.1203	−	42.2160i	−2.62825	−	1.51742i
$775$		0			0
$776$		−	25.2188i		−	0.905302i
$777$	−53.9730	−	14.0759i	−1.93627	−	0.504971i
$778$	−3.02314	−	19.0873i	−0.108385	−	0.684314i
$779$	−0.794514	−	0.0835068i	−0.0284664	−	0.00299194i
$780$		0			0
$781$	0.415297	+	3.95129i	0.0148605	+	0.141388i
$782$	7.37143	−	27.5106i	0.263602	−	0.983776i
$783$	−2.67045	+	16.8606i	−0.0954343	+	0.602548i
$784$	19.6256	−	27.7861i	0.700913	−	0.992362i
$785$		0			0
$786$	−1.74274	+	0.370432i	−0.0621616	+	0.0132129i
$787$	7.23632	+	11.1430i	0.257947	+	0.397204i	0.943790	−	0.330546i	$-0.107233\pi$
$787$	7.23632	+	11.1430i	0.257947	+	0.397204i	−0.685843	+	0.727750i	$0.740566\pi$
$788$	4.29616	+	6.61551i	0.153045	+	0.235668i
$789$	79.4852	−	16.8951i	2.82975	−	0.601481i
$790$		0			0
$791$	4.95194	−	11.3254i	0.176071	−	0.402686i
$792$	−6.10592	+	38.5512i	−0.216964	+	1.36986i
$793$	−0.179343	+	0.669316i	−0.00636865	+	0.0237681i
$794$	−6.35491	−	60.4629i	−0.225527	−	2.14575i
$795$		0			0
$796$	−2.70586	−	0.284397i	−0.0959066	−	0.0100802i
$797$	−6.01424	−	37.9724i	−0.213035	−	1.34505i	−0.829869	−	0.557959i	$-0.811585\pi$
$797$	−6.01424	−	37.9724i	−0.213035	−	1.34505i	0.616833	−	0.787094i	$-0.288415\pi$
$798$	18.9350	+	68.8223i	0.670290	+	2.43628i
$799$		−	9.07923i		−	0.321200i
$800$		0			0
$801$	3.87829	+	2.23913i	0.137033	+	0.0791159i
$802$	−0.345401	−	0.0181017i	−0.0121965	−	0.000639192i
$803$	5.27412	+	6.51300i	0.186120	+	0.229839i
$804$	0.771531	+	0.560550i	0.0272098	+	0.0197691i
$805$		0			0
$806$	−0.0898647	+	0.0652905i	−0.00316535	+	0.00229976i
$807$	54.6854	+	14.6529i	1.92502	+	0.515807i
$808$	20.3104	+	16.4471i	0.714519	+	0.578606i
$809$	−0.240260	+	1.13033i	−0.00844708	+	0.0397404i	−0.982169	−	0.187999i	$-0.939800\pi$
$809$	−0.240260	+	1.13033i	−0.00844708	+	0.0397404i	0.973722	+	0.227739i	$0.0731333\pi$
$810$		0			0
$811$	11.7589	+	3.82070i	0.412911	+	0.134163i	0.508104	−	0.861296i	$-0.330347\pi$
$811$	11.7589	+	3.82070i	0.412911	+	0.134163i	−0.0951926	+	0.995459i	$0.530347\pi$
$812$	−6.99369	−	1.05981i	−0.245430	−	0.0371920i
$813$	−6.95282	+	13.6457i	−0.243846	+	0.478575i
$814$	10.2118	+	48.0428i	0.357924	+	1.68390i
$815$		0			0
$816$	43.5196	+	9.25038i	1.52349	+	0.323828i
$817$	−25.5092	−	66.4538i	−0.892454	−	2.32492i
$818$	−36.5978	+	36.5978i	−1.27961	+	1.27961i
$819$	0.473433	+	1.04450i	0.0165431	+	0.0364977i
$820$		0			0
$821$	3.87750	−	36.8920i	0.135326	−	1.28754i	−0.690384	−	0.723443i	$-0.742558\pi$
$821$	3.87750	−	36.8920i	0.135326	−	1.28754i	0.825710	−	0.564095i	$-0.190775\pi$
$822$	−52.3428	−	20.0925i	−1.82567	−	0.700807i
$823$	−2.63210	+	50.2235i	−0.0917494	+	1.75068i	0.434790	+	0.900532i	$0.356823\pi$
$823$	−2.63210	+	50.2235i	−0.0917494	+	1.75068i	−0.526539	+	0.850151i	$0.676511\pi$
$824$	11.2156	+	19.4260i	0.390714	+	0.676737i
$825$		0			0
$826$	14.6929	−	16.5392i	0.511232	−	0.575472i
$827$	8.94542	+	17.5564i	0.311063	+	0.610495i	0.992620	−	0.121270i	$-0.0386968\pi$
$827$	8.94542	+	17.5564i	0.311063	+	0.610495i	−0.681557	+	0.731765i	$0.738697\pi$
$828$	−11.3750	+	9.21129i	−0.395308	+	0.320114i
$829$	20.7157	−	9.22321i	0.719485	−	0.320335i	−0.0141306	−	0.999900i	$-0.504498\pi$
$829$	20.7157	−	9.22321i	0.719485	−	0.320335i	0.733615	+	0.679565i	$0.237831\pi$
$830$		0			0
$831$	−6.56796	+	14.7519i	−0.227840	+	0.511737i
$832$	−0.286979	−	0.286979i	−0.00994922	−	0.00994922i
$833$	−12.5133	+	19.8448i	−0.433561	+	0.687582i
$834$	−60.5681	+	19.6798i	−2.09730	+	0.681454i
$835$		0			0
$836$	11.1278	−	10.0195i	0.384862	−	0.346531i
$837$	2.36368	−	1.53499i	0.0817008	−	0.0530571i
$838$	−0.898893	−	17.1519i	−0.0310518	−	0.592503i
$839$	−5.77620	+	17.7773i	−0.199417	+	0.613742i	0.800480	+	0.599360i	$0.204578\pi$
$839$	−5.77620	+	17.7773i	−0.199417	+	0.613742i	−0.999897	+	0.0143819i	$0.995422\pi$
$840$		0			0
$841$	3.31550	+	10.2041i	0.114328	+	0.351864i
$842$	−13.3267	+	5.11566i	−0.459270	+	0.176297i
$843$	6.04853	+	22.5734i	0.208323	+	0.777470i
$844$	−4.14647	+	0.435812i	−0.142728	+	0.0150013i
$845$		0			0
$846$	−11.5122	+	15.8452i	−0.395799	+	0.544770i
$847$	−0.534707	+	11.6989i	−0.0183727	+	0.401978i
$848$	50.9240	−	25.9471i	1.74874	−	0.891025i
$849$	−35.6995	+	20.6111i	−1.22520	+	0.707372i
$850$		0			0
$851$	20.2381	−	35.0534i	0.693752	−	1.20161i
$852$	−1.44950	−	0.941319i	−0.0496592	−	0.0322491i
$853$	33.5138	−	5.30806i	1.14749	−	0.181744i	0.446410	−	0.894828i	$-0.352702\pi$
$853$	33.5138	−	5.30806i	1.14749	−	0.181744i	0.701079	+	0.713084i	$0.252702\pi$
$854$	29.1458	+	9.25507i	0.997348	+	0.316702i
$855$		0			0
$856$	2.30334	+	1.02551i	0.0787264	+	0.0350513i
$857$	8.64649	−	2.31682i	0.295358	−	0.0791410i	−0.108097	−	0.994140i	$-0.534476\pi$
$857$	8.64649	−	2.31682i	0.295358	−	0.0791410i	0.403455	+	0.914999i	$0.367809\pi$
$858$	1.06277	−	1.31241i	0.0362823	−	0.0448049i
$859$	−15.4543	+	17.1638i	−0.527295	+	0.585621i	−0.946675	−	0.322190i	$-0.895581\pi$
$859$	−15.4543	+	17.1638i	−0.527295	+	0.585621i	0.419380	+	0.907811i	$0.362248\pi$
$860$		0			0
$861$	0.00633321	+	0.947241i	0.000215835	+	0.0322819i
$862$	8.84757	+	4.50806i	0.301349	+	0.153545i
$863$	−3.68178	+	0.192954i	−0.125329	+	0.00656823i	−0.114897	−	0.993377i	$-0.536654\pi$
$863$	−3.68178	+	0.192954i	−0.125329	+	0.00656823i	−0.0104318	+	0.999946i	$0.503321\pi$
$864$	−9.13923	−	10.1501i	−0.310923	−	0.345315i
$865$		0			0
$866$	−43.0183	−	38.7338i	−1.46182	−	1.31623i
$867$	15.5605	+	2.46454i	0.528463	+	0.0837003i
$868$	0.642582	+	0.975154i	0.0218107	+	0.0330989i
$869$	35.6731	+	49.0998i	1.21013	+	1.66560i
$870$		0			0
$871$	0.0220535	+	0.0495329i	0.000747253	+	0.00167836i
$872$	2.33657	−	6.08696i	0.0791261	−	0.206131i
$873$	27.5173	−	42.3729i	0.931318	−	1.43410i
$874$	−51.7975			−1.75208
$875$		0			0
$876$	−3.64571			−0.123177
$877$	16.3727	−	25.2117i	0.552866	−	0.851339i	−0.446183	−	0.894942i	$-0.647217\pi$
$877$	16.3727	−	25.2117i	0.552866	−	0.851339i	0.999049	+	0.0436027i	$0.0138836\pi$
$878$	15.1418	−	39.4459i	0.511013	−	1.33123i
$879$	12.2667	+	27.5515i	0.413746	+	0.929290i
$880$		0			0
$881$	−26.3597	−	36.2810i	−0.888079	−	1.22234i	−0.974117	−	0.226045i	$-0.927421\pi$
$881$	−26.3597	−	36.2810i	−0.888079	−	1.22234i	0.0860376	−	0.996292i	$-0.472579\pi$
$882$	47.0012	−	18.7669i	1.58261	−	0.631915i
$883$	28.6049	+	4.53057i	0.962631	+	0.152466i	0.617918	−	0.786242i	$-0.287976\pi$
$883$	28.6049	+	4.53057i	0.962631	+	0.152466i	0.344713	+	0.938708i	$0.387976\pi$
$884$	−0.151331	−	0.136259i	−0.00508980	−	0.00458287i
$885$		0			0
$886$	36.7226	+	40.7845i	1.23372	+	1.37018i
$887$	−24.0529	+	1.26056i	−0.807616	+	0.0423254i	−0.451674	−	0.892183i	$-0.649173\pi$
$887$	−24.0529	+	1.26056i	−0.807616	+	0.0423254i	−0.355942	+	0.934508i	$0.615840\pi$
$888$	41.8363	+	21.3167i	1.40394	+	0.715341i
$889$	22.1607	+	37.7976i	0.743246	+	1.26769i
$890$		0			0
$891$	6.50871	−	7.22865i	0.218050	−	0.242169i
$892$	−6.06596	+	7.49083i	−0.203103	+	0.250812i
$893$	−15.9494	+	4.27364i	−0.533728	+	0.143012i
$894$	−43.1735	−	19.2221i	−1.44394	−	0.642883i
$895$		0			0
$896$	−26.5972	+	24.2722i	−0.888552	+	0.810878i
$897$	−1.37455	+	0.217708i	−0.0458950	+	0.00726906i
$898$	24.2224	+	15.7302i	0.808312	+	0.524924i
$899$	−1.50825	+	2.61236i	−0.0503029	+	0.0871271i
$900$		0			0
$901$	−34.1351	+	19.7079i	−1.13720	+	0.656565i
$902$	0.743207	−	0.378683i	0.0247461	−	0.0126088i
$903$	−74.9445	+	38.8195i	−2.49400	+	1.29183i
$904$	−6.11603	+	8.41800i	−0.203416	+	0.279978i
$905$		0			0
$906$	−91.9096	+	9.66009i	−3.05349	+	0.320935i
$907$	−0.937438	−	3.49857i	−0.0311271	−	0.116168i	0.948614	−	0.316435i	$-0.102486\pi$
$907$	−0.937438	−	3.49857i	−0.0311271	−	0.116168i	−0.979741	+	0.200267i	$0.935819\pi$
$908$	7.73707	−	2.96998i	0.256764	−	0.0985623i
$909$	16.1797	+	49.7961i	0.536648	+	1.65163i
$910$		0			0
$911$	2.97054	−	9.14238i	0.0984183	−	0.302900i	−0.889711	−	0.456524i	$-0.849094\pi$
$911$	2.97054	−	9.14238i	0.0984183	−	0.302900i	0.988129	+	0.153623i	$0.0490943\pi$
$912$	−4.23481	−	80.8049i	−0.140228	−	2.67572i
$913$	−35.6309	+	23.1390i	−1.17921	+	0.765788i
$914$	10.2738	−	9.25056i	0.339827	−	0.305981i
$915$		0			0
$916$	2.46728	−	0.801669i	0.0815213	−	0.0264879i
$917$	−0.375004	+	0.996787i	−0.0123837	+	0.0329168i
$918$	15.3357	+	15.3357i	0.506154	+	0.506154i
$919$	2.99431	−	6.72533i	0.0987732	−	0.221848i	−0.857400	−	0.514651i	$-0.827921\pi$
$919$	2.99431	−	6.72533i	0.0987732	−	0.221848i	0.956173	+	0.292803i	$0.0945880\pi$
$920$		0			0
$921$	−28.7308	+	12.7918i	−0.946712	+	0.421503i
$922$	−33.3983	+	27.0454i	−1.09991	+	0.890693i
$923$	−0.0446111	−	0.0875541i	−0.00146839	−	0.00288188i
$924$	−13.2736	−	11.7918i	−0.436668	−	0.387923i
$925$		0			0
$926$	18.5411	+	32.1142i	0.609300	+	1.05534i
$927$	−2.35193	+	44.8776i	−0.0772476	+	1.47397i
$928$	13.6476	+	5.23882i	0.448004	+	0.171973i
$929$	6.12235	−	58.2502i	0.200868	−	1.91113i	−0.175194	−	0.984534i	$-0.556055\pi$
$929$	6.12235	−	58.2502i	0.200868	−	1.91113i	0.376062	−	0.926595i	$-0.377278\pi$
$930$		0			0
$931$	40.7514	+	12.6411i	1.33557	+	0.414294i
$932$	−11.3968	+	11.3968i	−0.373313	+	0.373313i
$933$	28.1324	+	73.2874i	0.921013	+	2.39932i
$934$	14.1324	+	3.00393i	0.462425	+	0.0982914i
$935$		0			0
$936$	−0.200710	−	0.944266i	−0.00656041	−	0.0308643i
$937$	−2.11148	+	4.14402i	−0.0689791	+	0.135379i	−0.922921	−	0.384989i	$-0.874205\pi$
$937$	−2.11148	+	4.14402i	−0.0689791	+	0.135379i	0.853942	+	0.520368i	$0.174205\pi$
$938$	2.22812	−	0.872432i	0.0727507	−	0.0284859i
$939$	−24.7274	−	8.03442i	−0.806948	−	0.262193i
$940$		0			0
$941$	−6.07308	+	28.5716i	−0.197977	+	0.931408i	0.761182	+	0.648539i	$0.224619\pi$
$941$	−6.07308	+	28.5716i	−0.197977	+	0.931408i	−0.959159	+	0.282869i	$0.908714\pi$
$942$	−41.1198	−	33.2981i	−1.33976	−	1.08491i
$943$	−0.663969	−	0.177910i	−0.0216218	−	0.00579355i
$944$	−20.2890	+	14.7408i	−0.660350	+	0.479773i
$945$		0			0
$946$	60.1267	+	43.6846i	1.95489	+	1.42031i
$947$	−3.83410	−	4.73472i	−0.124592	−	0.153858i	0.711033	−	0.703158i	$-0.248228\pi$
$947$	−3.83410	−	4.73472i	−0.124592	−	0.153858i	−0.835625	+	0.549301i	$0.814894\pi$
$948$	−26.3651	−	1.38174i	−0.856300	−	0.0448768i
$949$	−0.179507	−	0.103638i	−0.00582703	−	0.00336424i
$950$		0			0
$951$			21.3227i			0.691435i
$952$	13.8710	−	14.0578i	0.449563	−	0.455615i
$953$	0.872243	+	5.50713i	0.0282547	+	0.178393i	0.997780	−	0.0665986i	$-0.0212147\pi$
$953$	0.872243	+	5.50713i	0.0282547	+	0.178393i	−0.969525	+	0.244992i	$0.921215\pi$
$954$	84.5622	+	8.88785i	2.73780	+	0.287755i
$955$		0			0
$956$	0.0425472	+	0.404809i	0.00137607	+	0.0130925i
$957$	11.8696	−	44.2978i	0.383688	−	1.43194i
$958$	0.606690	−	3.83049i	0.0196013	−	0.123758i
$959$	−26.9809	+	19.8797i	−0.871259	+	0.641950i
$960$		0			0
$961$	−29.8354	+	6.34172i	−0.962433	+	0.204572i
$962$	−0.661614	−	1.01880i	−0.0213313	−	0.0328473i
$963$	2.75111	+	4.23634i	0.0886533	+	0.136514i
$964$	−0.702411	+	0.149302i	−0.0226231	+	0.00480869i
$965$		0			0
$966$	6.82809	+	61.0366i	0.219690	+	1.96382i
$967$	−9.25305	+	58.4215i	−0.297558	+	1.87871i	0.156414	+	0.987692i	$0.450007\pi$
$967$	−9.25305	+	58.4215i	−0.297558	+	1.87871i	−0.453972	+	0.891016i	$0.649993\pi$
$968$	2.55154	−	9.52247i	0.0820095	−	0.306064i
$969$	5.83307	+	55.4979i	0.187385	+	1.78285i
$970$		0			0
$971$	−52.4895	−	5.51687i	−1.68447	−	0.177045i	−0.786647	−	0.617404i	$-0.788185\pi$
$971$	−52.4895	−	5.51687i	−1.68447	−	0.177045i	−0.897822	+	0.440359i	$0.854851\pi$
$972$	1.83423	+	11.5809i	0.0588331	+	0.371458i
$973$	−9.60655	+	36.8355i	−0.307972	+	1.18089i
$974$			7.85203i			0.251595i
$975$		0			0
$976$	−30.0211	−	17.3327i	−0.960952	−	0.554806i
$977$	−13.1638	−	0.689886i	−0.421148	−	0.0220714i	−0.159415	−	0.987212i	$-0.550961\pi$
$977$	−13.1638	−	0.689886i	−0.421148	−	0.0220714i	−0.261733	+	0.965140i	$0.584294\pi$
$978$	40.3949	+	49.8835i	1.29168	+	1.59510i
$979$	−3.18912	−	2.31703i	−0.101925	−	0.0740525i
$980$		0			0
$981$	10.5677	−	7.67785i	0.337399	−	0.245135i
$982$	46.5975	+	12.4858i	1.48699	+	0.398436i
$983$	−41.7263	−	33.7893i	−1.33086	−	1.07771i	−0.990514	−	0.137413i	$-0.956121\pi$
$983$	−41.7263	−	33.7893i	−1.33086	−	1.07771i	−0.340350	−	0.940299i	$-0.610546\pi$
$984$	0.165789	−	0.779978i	0.00528518	−	0.0248648i
$985$		0			0
$986$	−22.0765	−	7.17309i	−0.703059	−	0.228438i
$987$	7.13844	+	18.2310i	0.227219	+	0.580299i
$988$	−0.168133	+	0.329979i	−0.00534902	+	0.0104980i
$989$	−12.7340	−	59.9086i	−0.404917	−	1.90498i
$990$		0			0
$991$	−10.3254	−	2.19474i	−0.327998	−	0.0697182i	0.0409694	−	0.999160i	$-0.486955\pi$
$991$	−10.3254	−	2.19474i	−0.327998	−	0.0697182i	−0.368968	+	0.929442i	$0.620289\pi$
$992$	−0.864924	−	2.25320i	−0.0274614	−	0.0715393i
$993$	1.99877	−	1.99877i	0.0634291	−	0.0634291i
$994$	−3.94976	+	1.79028i	−0.125279	+	0.0567843i
$995$		0			0
$996$	1.93185	−	18.3803i	0.0612131	−	0.582404i
$997$	55.8904	+	21.4543i	1.77007	+	0.679465i	0.999092	+	0.0425978i	$0.0135634\pi$
$997$	55.8904	+	21.4543i	1.77007	+	0.679465i	0.770974	+	0.636867i	$0.219770\pi$
$998$	3.29857	−	62.9405i	0.104414	−	1.99235i
$999$	15.4110	+	26.6927i	0.487584	+	0.844520i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	875.2.bb.c.493.5		288
5.2	odd	4		875.2.bb.a.507.5		288
5.3	odd	4		875.2.bb.b.507.14		288
5.4	even	2		175.2.x.a.3.14	✓	288
7.5	odd	6	inner	875.2.bb.c.243.14		288
25.6	even	5		875.2.bb.a.143.5		288
25.8	odd	20		175.2.x.a.17.5	yes	288
25.17	odd	20	inner	875.2.bb.c.857.14		288
25.19	even	10		875.2.bb.b.143.14		288
35.12	even	12		875.2.bb.a.257.5		288
35.19	odd	6		175.2.x.a.103.5	yes	288
35.33	even	12		875.2.bb.b.257.14		288
175.19	odd	30		875.2.bb.b.768.14		288
175.33	even	60		175.2.x.a.117.14	yes	288
175.117	even	60	inner	875.2.bb.c.607.5		288
175.131	odd	30		875.2.bb.a.768.5		288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.x.a.3.14	✓	288	5.4	even	2
175.2.x.a.17.5	yes	288	25.8	odd	20
175.2.x.a.103.5	yes	288	35.19	odd	6
175.2.x.a.117.14	yes	288	175.33	even	60
875.2.bb.a.143.5		288	25.6	even	5
875.2.bb.a.257.5		288	35.12	even	12
875.2.bb.a.507.5		288	5.2	odd	4
875.2.bb.a.768.5		288	175.131	odd	30
875.2.bb.b.143.14		288	25.19	even	10
875.2.bb.b.257.14		288	35.33	even	12
875.2.bb.b.507.14		288	5.3	odd	4
875.2.bb.b.768.14		288	175.19	odd	30
875.2.bb.c.243.14		288	7.5	odd	6	inner
875.2.bb.c.493.5		288	1.1	even	1	trivial
875.2.bb.c.607.5		288	175.117	even	60	inner
875.2.bb.c.857.14		288	25.17	odd	20	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 875 = 5^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	875.bb (of order \(60\), degree \(16\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.882496 + 1.35892i) q^{2} +(0.978941 - 2.55023i) q^{3} +(-0.254403 - 0.571398i) q^{4} +(2.60166 + 3.58087i) q^{6} +(2.64114 - 0.156130i) q^{7} +(-2.19977 - 0.348409i) q^{8} +(-3.31591 - 2.98566i) q^{9} +(2.62811 + 2.91881i) q^{11} +(-1.70624 + 0.0894203i) q^{12} +(-0.0865535 - 0.0441012i) q^{13} +(-2.11863 + 3.72689i) q^{14} +(3.25179 - 3.61148i) q^{16} +(-2.10918 + 2.60462i) q^{17} +(6.98356 - 1.87124i) q^{18} +(5.56832 + 2.47917i) q^{19} +(2.18736 - 6.88836i) q^{21} +(-6.28573 + 0.995562i) q^{22} +(4.39848 + 2.85640i) q^{23} +(-3.04197 + 5.26884i) q^{24} +(0.136313 - 0.0787005i) q^{26} +(-3.55840 + 1.81310i) q^{27} +(-0.761125 - 1.46942i) q^{28} +(2.51245 - 3.45809i) q^{29} +(-0.701840 + 0.0737664i) q^{31} +(0.885159 + 3.30346i) q^{32} +(10.0164 - 3.84493i) q^{33} +(-1.67814 - 5.16477i) q^{34} +(-0.862422 + 2.65426i) q^{36} +(-0.403914 - 7.70713i) q^{37} +(-8.28302 + 5.37906i) q^{38} +(-0.197199 + 0.177559i) q^{39} +(-0.124652 + 0.0405019i) q^{41} +(7.43042 + 9.05139i) q^{42} +(-8.25770 - 8.25770i) q^{43} +(0.999203 - 2.24425i) q^{44} +(-7.76327 + 3.45643i) q^{46} +(-2.10528 + 1.70482i) q^{47} +(-6.02679 - 11.8282i) q^{48} +(6.95125 - 0.824720i) q^{49} +(4.57761 + 7.92865i) q^{51} +(-0.00317989 + 0.0606759i) q^{52} +(10.9795 + 4.21462i) q^{53} +(0.676413 - 6.43564i) q^{54} +(-5.86430 - 0.576749i) q^{56} +(11.7735 - 11.7735i) q^{57} +(2.48206 + 6.46598i) q^{58} +(-5.04772 - 1.07293i) q^{59} +(-1.48307 - 6.97731i) q^{61} +(0.519128 - 1.01885i) q^{62} +(-9.22393 - 7.36783i) q^{63} +(3.97346 + 1.29105i) q^{64} +(-3.61445 + 17.0046i) q^{66} +(-0.433773 - 0.351262i) q^{67} +(2.02485 + 0.542557i) q^{68} +(11.5903 - 8.42087i) q^{69} +(0.818370 + 0.594581i) q^{71} +(6.25400 + 7.72305i) q^{72} +(2.13084 + 0.111673i) q^{73} +(10.8299 + 6.25262i) q^{74} -3.81243i q^{76} +(7.39691 + 7.29866i) q^{77} +(-0.0672616 - 0.424673i) q^{78} +(15.3675 + 1.61519i) q^{79} +(-0.258873 - 2.46301i) q^{81} +(0.0549659 - 0.205136i) q^{82} +(-1.69214 + 10.6837i) q^{83} +(-4.49246 + 0.502566i) q^{84} +(18.5090 - 3.93420i) q^{86} +(-6.35939 - 9.79260i) q^{87} +(-4.76429 - 7.33636i) q^{88} +(-0.981714 + 0.208670i) q^{89} +(-0.235485 - 0.102964i) q^{91} +(0.513159 - 3.23996i) q^{92} +(-0.498939 + 1.86207i) q^{93} +(-0.458824 - 4.36542i) q^{94} +(9.29110 + 0.976534i) q^{96} +(1.77133 + 11.1837i) q^{97} +(-5.01371 + 10.1740i) q^{98} -17.5251i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q + 8 q^{2} + 24 q^{3} - 10 q^{4} + 10 q^{7} + 36 q^{8} - 10 q^{9} - 6 q^{11} + 36 q^{12} - 20 q^{14} - 30 q^{16} + 42 q^{17} + 14 q^{18} - 30 q^{19} - 12 q^{21} - 32 q^{22} + 40 q^{23} - 48 q^{26}+ \cdots - 222 q^{98}+O(q^{100}) \) 288 * q + 8 * q^2 + 24 * q^3 - 10 * q^4 + 10 * q^7 + 36 * q^8 - 10 * q^9 - 6 * q^11 + 36 * q^12 - 20 * q^14 - 30 * q^16 + 42 * q^17 + 14 * q^18 - 30 * q^19 - 12 * q^21 - 32 * q^22 + 40 * q^23 - 48 * q^26 - 22 * q^28 - 18 * q^31 - 8 * q^32 + 30 * q^33 + 40 * q^36 + 10 * q^37 - 72 * q^38 + 30 * q^39 - 6 * q^42 + 108 * q^43 - 10 * q^44 - 6 * q^46 + 54 * q^47 - 16 * q^51 - 216 * q^52 - 50 * q^53 - 30 * q^54 + 4 * q^56 + 216 * q^57 + 4 * q^58 + 90 * q^59 - 18 * q^61 + 66 * q^63 - 100 * q^64 - 90 * q^66 - 4 * q^67 - 342 * q^68 - 24 * q^71 - 58 * q^72 + 6 * q^73 + 80 * q^77 + 132 * q^78 - 10 * q^79 - 10 * q^81 - 216 * q^82 + 20 * q^84 - 6 * q^86 + 48 * q^87 + 122 * q^88 + 120 * q^89 - 12 * q^91 + 4 * q^92 - 106 * q^93 - 30 * q^94 - 90 * q^96 - 222 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more